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

Author

Ron Knott, Jun 27 2013

Keywords

• nonn

Examples

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

Links

• Index entries for linear recurrences with constant coefficients, signature (3,6,-3,-1).

Crossrefs

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

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

Programs

Mathematica

Table[Fibonacci[n]^3 + Fibonacci[n+2]^3,{n,0,50}]
#[[1]]+#[[3]]&/@Partition[Fibonacci[Range[0,30]]^3,3,1] (* or *) LinearRecurrence[{3,6,-3,-1},{1,9,28,133},30] (* Harvey P. Dale, Jun 30 2025 *)

PARI

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

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))