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

Author

Michel Marcus, Jan 25 2017

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A000045, A007887, A080097.

Programs

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 *)

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

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