A298938
Number of ordered ways of writing n^3 as a sum of n squares of nonnegative integers.
Original entry on oeis.org
1, 1, 1, 4, 5, 686, 13942, 455988, 13617853, 454222894, 18323165948, 802161109047, 42149084452070, 2481730049781672, 157265294178424356, 10977302934685469078, 812821237985857557677, 64539935903231450294134, 5504599828399250884049308
Offset: 0
a(4) = 5 because we have [64, 0, 0, 0], [16, 16, 16, 16], [0, 64, 0, 0], [0, 0, 64, 0] and [0, 0, 0, 64].
Cf.
A000290,
A000578,
A006456,
A030273,
A037444,
A066535,
A218494,
A232173,
A287617,
A298329,
A298330,
A298935,
A298936,
A298939.
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Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^3}], {n, 0, 18}]
A299032
Number of ordered ways of writing n-th triangular number as a sum of n squares of positive integers.
Original entry on oeis.org
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
Offset: 0
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].
Cf.
A000217,
A000290,
A066535,
A072964,
A104383,
A126683,
A196010,
A224677,
A224679,
A278340,
A288126,
A298330,
A298858,
A298939,
A299031.
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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
-
Table[SeriesCoefficient[(-1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n (n + 1)/2}], {n, 0, 25}]
A319223
Number of ordered ways of writing n^3 as a sum of n squares.
Original entry on oeis.org
1, 2, 4, 32, 24, 14112, 674368, 39801344, 2454266992, 166591027058, 12820702401872, 1156778646258336, 119773060481140800, 14004241350957965408, 1791476464655904407168, 247572699435320047056384, 36696694077934168215974368, 5825316759916541565549586176, 989291135292653632945527984868
Offset: 0
-
Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n, {x, 0, n^3}], {n, 0, 18}]
Join[{1}, Table[SquaresR[n, n^3], {n, 18}]]
Showing 1-3 of 3 results.