A298939
Number of ordered ways of writing n^3 as a sum of n squares of positive integers.
Original entry on oeis.org
1, 1, 1, 4, 1, 286, 7582, 202028, 6473625, 226029577, 8338249868, 391526193477, 19990594900630, 1159906506684446, 74890158861242740, 5119732406649036418, 380146984328280974281, 30198665638519565614034, 2555354508318427693497565
Offset: 0
a(3) = 4 because we have [25, 1, 1], [9, 9, 9], [1, 25, 1] and [1, 1, 25].
Cf.
A000290,
A000578,
A006456,
A030273,
A037444,
A066535,
A218494,
A232173,
A287617,
A298329,
A298330,
A298935,
A298937,
A298938.
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Table[SeriesCoefficient[(-1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^3}], {n, 0, 18}]
A299031
Number of ordered ways of writing n-th triangular number as a sum of n squares of nonnegative integers.
Original entry on oeis.org
1, 1, 0, 3, 18, 60, 252, 1576, 10494, 64152, 458400, 3407019, 27713928, 225193982, 1980444648, 17626414158, 165796077562, 1593587604441, 15985672426992, 163422639872978, 1729188245991060, 18743981599820280, 208963405365941380, 2378065667103672024, 27742569814633730608
Offset: 0
a(3) = 3 because third triangular number is 6 and we have [4, 1, 1], [1, 4, 1] and [1, 1, 4].
Cf.
A000217,
A000290,
A066535,
A072964,
A104383,
A126683,
A196010,
A224677,
A224679,
A278340,
A288126,
A298329,
A298858,
A298938,
A299032.
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Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n (n + 1)/2}], {n, 0, 24}]
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.