|
MATHEMATICA
|
Table[
NextPartitions[n1_, n2_, n3_, n4_, n5_] :=
If[n1 < n, f[n1 + 1, n2, n3, n4, n5], 0] +
If[n2 < n1 - 1 || n2 === n - 1, f[n1, n2 + 1, n3, n4, n5], 0] +
If[n3 < n2 - 1 || n3 === n - 1 === n2 - 1, f[n1, n2, n3 + 1, n4, n5], 0] +
If[n4 < n3 - 1 || n4 === n - 1 === n3 - 1, f[n1, n2, n3, n4 + 1, n5], 0] +
If[n5 < n4 - 1, f[n1, n2, n3, n4, n5 + 1], 0];
pp = f[1, 0, 0, 0, 0];
Do[pp = Expand[pp /. f[ns__] :> NextPartitions[ns]], {5 n - 2}];
pp /. f[n, n, n, n, n - 1] -> 1,
|