A112961 a(n) = a(n-1)^3 + a(n-2)^3 for n >= 2 with a(0) = 0, a(1) = 1.

0, 1, 1, 2, 9, 737, 400316282, 64151935432803278787493321, 264015418305763603932856608512044494366944180663171458205345412119783805892929

Offset: 0

Author

Jonathan Vos Post, Jan 02 2006

Keywords

• easy
• nonn

Comments

A cubic Fibonacci sequence.

This is the cubic analog of the Fibonacci sequence analogously to A000283 being the quadratic analog of the Fibonacci sequence.

Examples

			a(3) = 1^3 + 1^3 = 2.
a(4) = 1^3 + 2^3 = 9.
a(5) = 2^3 + 9^3 = 737.
a(6) = 9^3 + 737^3 = 400316282.
		

Crossrefs

Cf. A000045, A000283.

Programs

Maple

a:= proc(n) a(n):= `if`(n<2, n, a(n-1)^3+a(n-2)^3) end:
seq(a(n), n=0..8);  # Alois P. Heinz, Sep 02 2023

Mathematica

RecurrenceTable[{a[1]==a[2]==1,a[n]==a[n-1]^3+a[n-2]^3},a,{n,10}] (* Harvey P. Dale, Aug 24 2014 *)

Formula

a(n) ~ b^3^n with b = 1.0275436477.... [Charles R Greathouse IV, Dec 28 2011]

Extensions

Name edited by Petros Hadjicostas, Nov 03 2019

a(0)=0 prepended by Alois P. Heinz, Sep 02 2023