|
| |
|
|
A098531
|
|
Sum of fifth powers of first n Fibonacci numbers.
|
|
8
| |
|
|
0, 1, 2, 34, 277, 3402, 36170, 407463, 4491564, 49926988, 553211363, 6137270812, 68054635036, 754774491429, 8370420537086, 92830050637086, 1029498223070793, 11417322172518550, 126619992693837974, 1404237451180502875
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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
|
|
|
FORMULA
| 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)
|
|
|
MATHEMATICA
| Accumulate[Fibonacci[Range[0, 20]]^5] [From Harvey P. Dale, Jan. 14, 2011]
|
|
|
PROG
| (PARI) a(n)=sum(i=0, n, fibonacci(i)^5)
|
|
|
CROSSREFS
| Cf. A001654, A005968, A005969, A098532, A098533.
Cf. A056572.
Cf. A047650.
Cf. A119286, A000071, A001654, A005968, A005969, A098532, A098533, A128697.
Sequence in context: A131471 A036827 A136362 * A092408 A180764 A005261
Adjacent sequences: A098528 A098529 A098530 * A098532 A098533 A098534
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 12 2004
|
| |
|
|
