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}]
A298936
Number of ordered ways of writing n^2 as a sum of n nonnegative cubes.
Original entry on oeis.org
1, 1, 0, 6, 6, 20, 120, 7, 1689, 6636, 36540, 64020, 963996, 2894892, 19555965, 176079995, 955611188, 6684303780, 42462792168, 292378003753, 1886275214112, 13384059605364, 87399249887334, 624073002367892, 5080120229014734, 37587589611771480
Offset: 0
a(3) = 6 because we have [8, 1, 0], [8, 0, 1], [1, 8, 0], [1, 0, 8], [0, 8, 1] and [0, 1, 8].
Cf.
A000290,
A000578,
A023358,
A030272,
A218495,
A259792,
A291700,
A298671,
A298672,
A298934,
A298937.
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f:= n -> coeff(add(x^(k^3),k=0..floor(n^(2/3)))^n,x,n^2):
map(f, [$0..30]); # Robert Israel, Jan 29 2018
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Table[SeriesCoefficient[Sum[x^k^3, {k, 0, Floor[n^(2/3) + 1]}]^n, {x, 0, n^2}], {n, 0, 25}]
Showing 1-2 of 2 results.