A200408 a(n) = -4 + 5*Fibonacci(n+1)^2.

1, 1, 16, 41, 121, 316, 841, 2201, 5776, 15121, 39601, 103676, 271441, 710641, 1860496, 4870841, 12752041, 33385276, 87403801, 228826121, 599074576, 1568397601, 4106118241, 10749957116, 28143753121, 73681302241, 192900153616, 505019158601, 1322157322201

Offset

0,3

Comments

a(1) and a(2n) are perfect squares.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).

Formula

a(n) = 3*a(n-1)-3*a(n-3)+a(n-4). G.f.: 1-x*(x^3-7*x^2+13*x+1) / ((x-1)*(x+1)*(x^2-3*x+1)). - Colin Barker, Sep 01 2013

a(n) = A005248(n+1) - A010696(n). - R. J. Mathar, Jan 18 2021

Mathematica

Table[-4 + 5*Fibonacci[n]^2, {n, 2, 31}] (* Alonso del Arte, Nov 17 2011 *)

Prog

(PARI) Vec(-x*(x^3-7*x^2+13*x+1)/((x-1)*(x+1)*(x^2-3*x+1)) + O(x^100)) \\ Colin Barker, Sep 01 2013

Crossrefs

Cf. A005248.

Sequence in context: A188861 A134593 A227816 * A280184 A228685 A317761

Adjacent sequences: A200405 A200406 A200407 * A200409 A200410 A200411

Keyword

nonn,easy

Author

Artur Jasinski, Nov 17 2011

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 11 2024

Status

approved