A247599 - OEIS

%I #24 May 01 2022 14:00:41

%S 1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,3,2,2,1,3,2,2,1,4,2,2,2,4,3,2,2,5,4,

%T 3,3,4,3,2,2,6,4,4,4,4,3,2,3,7,5,4,4,4,3,3,4,8,5,5,6,4,4,4,4,10,6,8,7,

%U 6,5,6,5,10,5,8,7,6,4,6,4,12,8,8,8,8,7

%N Number of ways of writing n as a sum: n = 2^0*k(0)^3 + 2^1*k(1)^3 + 2^2*k(2)^3 + ... where the k's are nonnegative integers.

%H Alois P. Heinz, <a href="/A247599/b247599.txt">Table of n, a(n) for n = 0..10000</a>

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p       `if`(n<0 or i<0, 0, add(b(n-2^i*j^3, i-1),

%p            j=0..iroot(iquo(n, 2^i), 3))))

%p     end:

%p a:= n-> b(n, ilog2(n)):

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Dec 28 2014

%t b[n_, i_] := b[n, i] = If[n == 0, 1,

%t      If[n < 0 || i < 0, 0, Sum[b[n - 2^i*j^3, i - 1],

%t        {j, 0, Floor@Quotient[n, 2^i]^(1/3)}]]];

%t a[n_] := b[n, Floor@Log2[n]];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 01 2022, after _Alois P. Heinz_ *)

%K nonn,look

%O 0,9

%A _David S. Newman_, Sep 21 2014