A025453 - OEIS

%I #17 Jan 23 2025 12:40:30

%S 1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,2,2,

%T 2,3,2,2,1,1,2,2,2,2,2,1,1,1,2,2,1,2,1,1,2,2,3,2,2,2,2,2,2,2,3,3,2,3,

%U 3,2,3,2,4,2,2,3,2,2,2,2,2,3,3,3,3,2,3,2,2,3,2,4,3,3,3,2,3,3,3,3,3,2,2,2,2,3,2,3

%N Number of partitions of n into 9 nonnegative cubes.

%H David A. Corneth, <a href="/A025453/b025453.txt">Table of n, a(n) for n = 0..10000</a>

%e a(8) = 2 via 8*0^3 + 1*2^3 = 1 * 0^3 + 8*1^3.

%p f:= proc(x,m,M)

%p local i;

%p option remember;

%p   if x = 0 then return 1

%p   elif m = 0 then return 0

%p   fi;

%p   add(procname(x-i^3, m-1, i), i=1..min(M,floor(x^(1/3))));

%p end proc:

%p map(f, [$0..150],9,150); # _Robert Israel_, Jan 23 2025

%o (PARI) first(n) = my(v=vector(n), maxb=sqrtnint(n, 3)); forvec(x=vector(9, i, [0, maxb]), s=sum(i=1, 9, x[i]^3); if(0<s && s<=n, v[s]++); , 1); concat(1, v) \\ _David A. Corneth_, Jan 23 2025

%Y Cf. A025446, A025447, A025448, A025449, A025450, A025451, A025452, this sequence, A025454.

%K nonn

%O 0,9

%A _David W. Wilson_