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A299032 Number of ordered ways of writing n-th triangular number as a sum of n squares of positive integers. 3
1, 1, 0, 3, 6, 0, 12, 106, 420, 2718, 18240, 120879, 694320, 5430438, 40668264, 300401818, 2369504386, 19928714475, 174151735920, 1543284732218, 14224347438876, 135649243229688, 1331658133954940, 13369350846412794, 138122850643702056, 1462610254141337590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Index entries for sequences related to sums of squares

Index to sequences related to polygonal numbers

FORMULA

a(n) = [x^(n*(n+1)/2)] (Sum_{k>=1} x^(k^2))^n.

EXAMPLE

a(4) = 6 because fourth triangular number is 10 and we have [4, 4, 1, 1], [4, 1, 4, 1], [4, 1, 1, 4], [1, 4, 4, 1], [1, 4, 1, 4] and [1, 1, 4, 4].

MAPLE

b:= proc(n, t) option remember; local i; if n=0 then

      `if`(t=0, 1, 0) elif t<1 then 0 else 0;

      for i while i^2<=n do %+b(n-i^2, t-1) od; % fi

    end:

a:= n-> b(n*(n+1)/2, n):

seq(a(n), n=0..25);  # Alois P. Heinz, Feb 05 2018

MATHEMATICA

Table[SeriesCoefficient[(-1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n (n + 1)/2}], {n, 0, 25}]

CROSSREFS

Cf. A000217, A000290, A066535, A072964, A104383, A126683, A196010, A224677, A224679, A278340, A288126, A298330, A298858, A298939, A299031.

Sequence in context: A287845 A070297 A284896 * A094674 A125287 A264813

Adjacent sequences:  A299029 A299030 A299031 * A299033 A299034 A299035

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 01 2018

STATUS

approved

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Last modified January 26 20:42 EST 2020. Contains 331288 sequences. (Running on oeis4.)