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A025453 Number of partitions of n into 9 nonnegative cubes.

%I A025453 #17 Jan 23 2025 12:40:30
%S A025453 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 A025453 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 A025453 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 A025453 Number of partitions of n into 9 nonnegative cubes.
%H A025453 David A. Corneth, <a href="/A025453/b025453.txt">Table of n, a(n) for n = 0..10000</a>
%e A025453 a(8) = 2 via 8*0^3 + 1*2^3 = 1 * 0^3 + 8*1^3.
%p A025453 f:= proc(x,m,M)
%p A025453 local i;
%p A025453 option remember;
%p A025453   if x = 0 then return 1
%p A025453   elif m = 0 then return 0
%p A025453   fi;
%p A025453   add(procname(x-i^3, m-1, i), i=1..min(M,floor(x^(1/3))));
%p A025453 end proc:
%p A025453 map(f, [$0..150],9,150); # _Robert Israel_, Jan 23 2025
%o A025453 (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 A025453 Cf. A025446, A025447, A025448, A025449, A025450, A025451, A025452, this sequence, A025454.
%K A025453 nonn
%O A025453 0,9
%A A025453 _David W. Wilson_