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Search: id:A098531
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| A098531 |
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Sum of fifth powers of first n Fibonacci numbers. |
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+0
9
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| 0, 1, 2, 34, 277, 3402, 36170, 407463, 4491564, 49926988, 553211363, 6137270812, 68054635036, 754774491429, 8370420537086, 92830050637086, 1029498223070793, 11417322172518550, 126619992693837974, 1404237451180502875
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OFFSET
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0,3
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COMMENT
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Prime p divides a((p-1)/2) for p = {29,89,101,181,229,...} = A047650[n] Primes for which golden mean tau is a quadratic residue or Primes of the form x^2 + 20y^2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 07 2006
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FORMULA
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a(n)=(1/275)*(F(5n+1)+4*F(5n+2)-(-1)^n*(55/2)*F(3n+1)-110*F(n+2)+175/2) where F(n)=A000045(n)
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PROGRAM
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(PARI) a(n)=sum(i=0, n, fibonacci(i)^5)
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CROSSREFS
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Cf. A001654, A005968, A005969, A098532, A098533.
Cf. A056572.
Cf. A047650.
Cf. A119286, A000071, A001654, A005968, A005969, A098532, A098533, A128697.
Adjacent sequences: A098528 A098529 A098530 this_sequence A098532 A098533 A098534
Sequence in context: A131471 A036827 A136362 this_sequence A092408 A005261 A104898
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 12 2004
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