A281619 Integer values of (A000045^2-1)/9 where A000045(m) is the m-th Fibonacci number.

0, 7, 336, 880, 6032, 15792, 741895, 34853280, 91247072, 625416736, 1637362272, 76921173511, 3613657792752, 9460678925136, 64844458022832, 169764995085840, 7975341111241735, 374671267233275712, 980902112224710592, 6723203096097857600, 17601574218852716736, 826899317018844410887

Offset

1,2

Comments

Also the integer values of A080097/9 where A080097(m) = Fibonacci(n+2)^2 - 1.

The indices of the Fibonacci numbers are 1, 2, 6, 10, and 11 mod 12. See the Wulczy link.

Links

Robert Israel, Table of n, a(n) for n = 1..997

G. Wulczy, Unity with Fibonacci, Problem H-247 and solution, Fib. Quarter. p. 89_90, Vol 15, 1, Feb. 1977.

Formula

G.f.: x^2*(7*x^10+336*x^9+880*x^8+6032*x^7+15792*x^6+16114*x^5+15792*x^4

+6032*x^3+880*x^2+336*x+7)/(-x^15+103683*x^10-103683*x^5+1). - Robert Israel, Mar 05 2017

Maple

seq(seq((combinat:-fibonacci(12*m+j)^2-1)/9, j=[2, 6, 10, 11, 13]), m=0..20); # Robert Israel, Mar 05 2017

Mathematica

Select[(#^2-1)/9&/@Fibonacci[Range[100]], IntegerQ] (* Harvey P. Dale, Feb 07 2017 *)

Prog

(PARI) lista(nn)=v = [1, 2, 6, 10, 11, 13, 14, 18, 22, 23]; for (n=1, nn, j = (n % #v) +1; k = n\#v; print1((fibonacci(24*k+v[j])^2-1)/9, ", "); );
(PARI) a(n)=fibonacci(n\5*12+[1, 2, 6, 10, 11][n%5+1])^2\9 \\ Charles R Greathouse IV, Jan 26 2017

Crossrefs

Cf. A000045, A007887, A080097.

Sequence in context: A160432 A324233 A009587 * A054325 A161582 A200967

Adjacent sequences: A281616 A281617 A281618 * A281620 A281621 A281622

Keyword

nonn,easy

Author

Michel Marcus, Jan 25 2017

Status

approved