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 A229239 Total number of parts in all partitions of n^2 into squares. 3
 0, 1, 5, 19, 64, 206, 616, 1766, 4836, 12910, 33248, 83768, 205693, 495357, 1169030, 2713262, 6193247, 13932454, 30905452, 67684181, 146439145, 313266730, 663004212, 1389106622, 2882712626, 5928222338, 12086570971, 24440494114, 49035791349, 97646904849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..689 (terms 0..200 from Alois P. Heinz) Christopher Hunt Gribble, C++ program EXAMPLE a(2) = 5 because there are 5 parts in the set of partitions of 2^2 into squares. The partitions are (1 2 X 2 square) and (4 1 X 1 squares) giving 5 parts in all. MAPLE b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0\$2], b(n, i-1)+`if`(i^2>n, [0\$2], (g->g+[0, g[1]])(b(n-i^2, i))))) end: a:= n-> b(n^2, n)[2]: seq(a(n), n=0..40); # Alois P. Heinz, Sep 23 2013 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + If[ i^2 > n, {0, 0}, Function[g, g + {0, g[[1]]}][b[n - i^2, i]]]]]; a[n_] := b[n^2, n][[2]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *) CROSSREFS Row sums of A229468. Cf. A037444. Sequence in context: A211842 A304134 A318946 * A296330 A304162 A001870 Adjacent sequences: A229236 A229237 A229238 * A229240 A229241 A229242 KEYWORD nonn AUTHOR Christopher Hunt Gribble, Sep 23 2013 STATUS approved

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Last modified October 2 09:28 EDT 2023. Contains 365833 sequences. (Running on oeis4.)