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   A029745 Expansion of (1+2x+6x^2+x^3)/(1-2x^2). 1
   1, 2, 8, 5, 16, 10, 32, 20, 64, 40, 128, 80, 256, 160, 512, 320, 1024, 640, 2048, 1280, 4096, 2560, 8192, 5120, 16384, 10240, 32768, 20480, 65536, 40960, 131072, 81920, 262144, 163840, 524288, 327680, 1048576, 655360, 2097152, 1310720, 4194304 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,2 COMMENTS Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k. Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k. LINKS Index entries for linear recurrences with constant coefficients, signature (0,2) FORMULA G.f.: (1+2x+6x^2+x^3)/(1-2x^2). MATHEMATICA LinearRecurrence[{0, 2}, {1, 2, 8, 5}, 50] (* or *) With[{nn=20}, Join[{1, 2}, Riffle[ 8*2^Range[0, nn], 5 2^Range[0, nn]]]] (* Harvey P. Dale, Sep 28 2016 *) PROG (PARI) a(n)=if(n<2, 1+max(-1, n), 2^(n\2)*if(n%2, 5/2, 4)) CROSSREFS Cf. A094958 (numbers of the form 2^n or 5*2^n) Sequence in context: A182528 A185583 A155901 * A183232 A096417 A274416 Adjacent sequences:  A029742 A029743 A029744 * A029746 A029747 A029748 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by T. D. Noe, Nov 12 2010 STATUS approved
  
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explanation: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) and describes the integer sequence A029745. It includes the expansion of a generating function, comments, formulas, and programming code for generating the sequence. The text does not contain a specific math question or a question and answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: This site is supported by donations to The OEIS Foundation.
  
   Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate
  
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   A029745 Expansion of (1+2x+6x^2+x^3)/(1-2x^2). 1
   1, 2, 8, 5, 16, 10, 32, 20, 64, 40, 128, 80, 256, 160, 512, 320, 1024, 640, 2048, 1280, 4096, 2560, 8192, 5120, 16384, 10240, 32768, 20480, 65536, 40960, 131072, 81920, 262144, 163840, 524288, 327680, 1048576, 655360, 2097152, 1310720, 4194304 (list; graph; refs; listen; history; text; internal format)
   OFFSET 1,2 COMMENTS Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k. Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k. LINKS Index entries for linear recurrences with constant coefficients, signature (0,2) FORMULA G.f.: (1+2x+6x^2+x^3)/(1-2x^2). MATHEMATICA LinearRecurrence[{0, 2}, {1, 2, 8, 5}, 50] (* or *) With[{nn=20}, Join[{1, 2}, Riffle[ 8*2^Range[0, nn], 5 2^Range[0, nn]]]] (* Harvey P. Dale, Sep 28 2016 *) PROG (PARI) a(n)=if(n<2, 1+max(-1, n), 2^(n\2)*if(n%2, 5/2, 4)) CROSSREFS Cf. A094958 (numbers of the form 2^n or 5*2^n) Sequence in context: A182528 A185583 A155901 * A183232 A096417 A274416 Adjacent sequences:  A029742 A029743 A029744 * A029746 A029747 A029748 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by T. D. Noe, Nov 12 2010 STATUS approved
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an excerpt from the Online Encyclopedia of Integer Sequences (OEIS) and describes the integer sequence A029745. It includes the expansion of a generating function, comments, formulas, and programming code for generating the sequence. The text does not contain a specific math question or a question and answer.
  
  Label: no-question