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a(n) = a(n-1)^3 + a(n-2)^3 for n >= 2 with a(0) = 0, a(1) = 1.
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%I #21 Sep 15 2023 12:00:11

%S 0,1,1,2,9,737,400316282,64151935432803278787493321,

%T 264015418305763603932856608512044494366944180663171458205345412119783805892929

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

%C A cubic Fibonacci sequence.

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

%F a(n) ~ b^3^n with b = 1.0275436477.... [_Charles R Greathouse IV_, Dec 28 2011]

%e a(3) = 1^3 + 1^3 = 2.

%e a(4) = 1^3 + 2^3 = 9.

%e a(5) = 2^3 + 9^3 = 737.

%e a(6) = 9^3 + 737^3 = 400316282.

%p a:= proc(n) a(n):= `if`(n<2, n, a(n-1)^3+a(n-2)^3) end:

%p seq(a(n), n=0..8); # _Alois P. Heinz_, Sep 02 2023

%t 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 *)

%Y Cf. A000045, A000283.

%K easy,nonn

%O 0,4

%A _Jonathan Vos Post_, Jan 02 2006

%E Name edited by _Petros Hadjicostas_, Nov 03 2019

%E a(0)=0 prepended by _Alois P. Heinz_, Sep 02 2023