A092362 Number of partitions of n^2 into squares greater than 1.

1, 0, 1, 1, 2, 3, 5, 8, 11, 28, 44, 94, 167, 354, 643, 1314, 2412, 4792, 8981, 17374, 32566, 62008, 115702, 217040, 402396, 745795, 1372266, 2517983, 4595652, 8354350, 15125316, 27265107, 48972467, 87584837, 156119631, 277152178, 490437445, 864534950

Offset

0,5

Comments

a(n) = A078134(A000290(n)).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

a(n) ~ exp(3*Pi^(1/3) * Zeta(3/2)^(2/3) * n^(2/3) / 2^(4/3)) * Zeta(3/2)^(4/3) / (2^(11/3) * sqrt(3) * Pi^(5/6) * n^(11/3)). - Vaclav Kotesovec, Apr 10 2017

Example

a(6) = 5: 6^2 = 36 = 16+16+4 = 16+4+4+4+4+4 = 9+9+9+9 = 4+4+4+4+4+4+4+4+4.

Maple

b:=proc(n, i) option remember; `if`(n=0, 1,
     `if`(i<2, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))
   end:
a:= n-> b(n^2, n):
seq(a(n), n=0..50);  # Alois P. Heinz, Apr 15 2013

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, b[n, i-1] + If[i^2>n, 0, b[n-i^2, i]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Crossrefs

Cf. A001156, A037444.

Cf. A093115, A093116.

Sequence in context: A332070 A334741 A259973 * A105766 A056695 A342746

Adjacent sequences: A092359 A092360 A092361 * A092363 A092364 A092365

Keyword

nonn

Author

Reinhard Zumkeller, Mar 19 2004

Extensions

Corrected a(0) and more terms from Alois P. Heinz, Apr 15 2013

Status

approved