A073336 Total number of square parts in all partitions of n.

0, 1, 2, 4, 8, 13, 21, 33, 51, 76, 111, 159, 226, 315, 435, 593, 805, 1077, 1435, 1893, 2486, 3237, 4198, 5405, 6935, 8843, 11235, 14201, 17893, 22437, 28052, 34929, 43371, 53653, 66201, 81410, 99876, 122155, 149063, 181399, 220280, 266811, 322524, 388960

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

Formula

a(n) = Sum_{k=1..n} A046951(k)*A000041(n-k).

G.f.: Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) / Product_{j>=1} (1 - x^j). - Ilya Gutkovskiy, Jan 24 2017

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(i<1, [0, 0], add((l->l+[0, `if`(j>0 and issqr(i),
       l[1]*j, 0)])(b(n-i*j, i-1)), j=0..iquo(n, i))))
    end:
a:= n-> b(n, n)[2] :
seq(a(n), n=0..60);  # Alois P. Heinz, Feb 19 2013

Mathematica

b[n_, i_] :=  b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, Sum[Function[{l}, l+{0, If[j>0 && IntegerQ[Sqrt[i]], l[[1]]*j, 0]}][b[n-i*j, i-1]], {j, 0, Quotient[n, i]}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, May 13 2015, after Alois P. Heinz *)

Crossrefs

Cf. A000041, A046951, A309535.

Sequence in context: A349061 A241691 A164429 * A164420 A164457 A164419

Adjacent sequences: A073333 A073334 A073335 * A073337 A073338 A073339

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 22 2002

Extensions

More terms from Emeric Deutsch, Nov 18 2004

a(0) inserted by Alois P. Heinz, Feb 19 2013

Status

approved