A332716 - OEIS

%I #18 Oct 31 2022 06:26:29

%S 1,1,5,149,20569,11749641,26649774581,236837126431501,

%T 8237168505776637425,1125036467745713090813969,

%U 606147434557459526483161067501,1293596348252277644272081532560154645,10970544241076481629439275072320816659677161

%N Number of compositions of n^2 where each part is less than or equal to n.

%C All terms are odd.

%H Alois P. Heinz, <a href="/A332716/b332716.txt">Table of n, a(n) for n = 0..57</a>

%F a(n) = Sum_{i=0..n-1} A048004(n^2-1,i) for i > 0.

%e a(2) = 5: 22, 211, 121, 112, 1111.

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

%p       add(b(n-d, k), d=1..min(n, k)))

%p     end:

%p a:= n-> b(n^2, n):

%p seq(a(n), n=0..15);

%t b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - d, k], {d, 1, Min[n, k]}]];

%t a[n_] := b[n^2, n];

%t Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Oct 31 2022, after _Alois P. Heinz_ *)

%Y Cf. A000079, A000290, A008464, A048004, A090667, A103488, A332721, A332796.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 20 2020