A226976 Fibonacci(n)^3 + Fibonacci(n+2)^3

1, 9, 28, 133, 539, 2322, 9773, 41501, 175636, 744273, 3152359, 13354306, 56568617, 239630337, 1015087436, 4299984173, 18215017507, 77160064914, 326855259829, 1384581132277, 5865179743556, 24845300179929, 105246380344463, 445830821750018, 1888569667033489

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = 3a(n-1)+6a(n-2)-3a(n-3)-a(n-4)

G.f.: (1+6x-5x^2-2x^3)/(1-3x-6x^2+3x^3+x^4)= (2x^2+7x+1)(1-x)/((x^2-x-1)(x^2+4x-1))

Example

a(2) = Fibonacci(2)^3 + Fibonacci(4)^3 = 1^3 + 2^3 = 9

Mathematica

Table[Fibonacci[n]^3 + Fibonacci[n+2]^3, {n, 0, 50}]

Prog

(PARI) a(n) = fibonacci(n)^3+fibonacci(n+2)^3; \\ Joerg Arndt, Jul 07 2013

Crossrefs

Cf. A000045 (Fibonacci), A056570 (Fibonacci^3).

Cf. A110224 (Fib(n)^3 + Fib(n+1)^3).

Sequence in context: A198059 A181090 A073706 * A042501 A271185 A306843

Adjacent sequences: A226973 A226974 A226975 * A226977 A226978 A226979

Keyword

nonn

Author

Ron Knott, Jun 27 2013

Status

approved