A344708 Number of partitions of n^2 into a square number of square parts.

1, 1, 2, 2, 3, 5, 10, 16, 30, 65, 126, 248, 527, 1024, 2061, 4310, 8213, 16367, 33041, 63217, 122919, 242242, 458198, 877519, 1685444, 3159685, 5944954, 11204470, 20745676, 38471990, 71245358, 130408025, 238462989, 435146790, 787184098, 1421400530, 2559536132

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Example

a(5) = 5: [25], [16,4,4,1], [9,9,1,1,1,1,1,1,1], [4,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].

Maple

s:= n-> issqr(n):
h:= proc(n) option remember; `if`(s(n), n, h(n-1)) end:
b:= proc(n, i, c) option remember; `if`(n=0 or i=1, `if`(
      s(c+n), 1, 0), b(n-i, h(min(n-i, i)), c+1)+b(n, h(i-1), c))
    end:
a:= n-> b(n^2$2, 0):
seq(a(n), n=0..40);

Mathematica

s[n_] := IntegerQ@Sqrt[n];
h[n_] := h[n] = If[s[n], n, h[n - 1]];
b[n_, i_, c_] := b[n, i, c] = If[n == 0 || i == 1, If[s[c + n], 1, 0],
     b[n - i, h[Min[n - i, i]], c + 1] + b[n, h[i - 1], c]];
a[n_] := b[n^2, n^2, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 25 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000290.

Sequence in context: A130377 A260956 A360299 * A322113 A153900 A049873

Adjacent sequences: A344705 A344706 A344707 * A344709 A344710 A344711

Keyword

nonn

Author

Alois P. Heinz, May 26 2021

Status

approved