A184298 Number of strings of numbers x(i=1..n) in 0..4 with sum i^3*x(i)^2 equal to n^3*16.

1, 1, 1, 2, 1, 5, 19, 65, 179, 567, 1971, 7188, 24104, 86560, 307758, 1093010, 3680499, 12984253, 44872804, 155894872, 524533909, 1798853267, 6095276268, 20640244000, 68424020576, 228663331673, 756885973017, 2497335148084, 8126657372315, 26483584838833, 85638964006761, 275736953129009

Offset

1,4

Comments

Column 4 of A184303

Links

Robert Israel, Table of n, a(n) for n = 1..60

Example

All solutions for n=5
..0
..0
..0
..0
..4

Maple

F:= proc(n, t) option remember;
   local k, r;
   if t < 0 or t > 4*(n+1)^2*n^2 then return 0 fi;
   if n = 1 then if member(t, [0, 1, 4, 9, 16]) then return 1 else return 0 fi fi;
   add(procname(n-1, t - n^3*k^2), k=0..4);
end proc:
seq(F(n, 16*n^3), n=1..33); # Robert Israel, Apr 18 2019

Mathematica

F[n_, t_] := F[n, t] = If[t<0 || t>4(n+1)^2*n^2, 0, If[n == 1, If[MemberQ[ {0, 1, 4, 9, 16}, t], 1, 0], Sum[F[n-1, t - n^3*k^2], {k, 0, 4}]]];
Table[F[n, 16*n^3], {n, 1, 33}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)

Crossrefs

Sequence in context: A013014 A012905 A254677 * A349852 A260701 A184300

Adjacent sequences: A184295 A184296 A184297 * A184299 A184300 A184301

Keyword

nonn

Author

R. H. Hardin, Jan 10 2011

Extensions

a(24)-a(32) from Robert Israel, Apr 18 2019

Status

approved