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 A303484 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = [x^(n^3)] (1/(1 - x))*(Sum_{j>=0} x^(j^3))^k. 1
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 11, 11, 5, 1, 1, 6, 20, 30, 18, 6, 1, 1, 7, 37, 84, 66, 26, 7, 1, 1, 8, 70, 237, 241, 115, 37, 8, 1, 1, 9, 135, 662, 853, 500, 200, 50, 9, 1, 1, 10, 264, 1780, 2847, 2093, 1012, 302, 63, 10, 1, 1, 11, 520, 4536, 9033, 8451, 4914, 1769, 441, 80, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A(n,k) is the number of nonnegative solutions to (x_1)^3 + (x_2)^3 + ... + (x_k)^3 <= n^3. LINKS Table of n, a(n) for n=0..77. Index entries for sequences related to sums of cubes EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, 6, ... 1, 3, 6, 11, 20, 37, ... 1, 4, 11, 30, 84, 237, ... 1, 5, 18, 66, 241, 853, ... 1, 6, 26, 115, 500, 2093, ... MATHEMATICA Table[Function[k, SeriesCoefficient[1/(1 - x) Sum[x^i^3, {i, 0, n}]^k, {x, 0, n^3}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten CROSSREFS Columns k=0..4 give A000012, A000027, A224214, A224215. Main diagonal gives A303169. Cf. A290054, A302998. Sequence in context: A119724 A162424 A302998 * A008571 A230860 A051137 Adjacent sequences: A303481 A303482 A303483 * A303485 A303486 A303487 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Apr 24 2018 STATUS approved

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)