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 A297930 Number of partitions of n into 2 squares and 2 nonnegative cubes. 1
 1, 2, 3, 2, 2, 2, 2, 1, 2, 4, 5, 3, 2, 3, 2, 1, 3, 5, 6, 3, 3, 3, 2, 0, 2, 5, 6, 5, 4, 5, 2, 2, 4, 5, 6, 4, 6, 6, 4, 2, 4, 6, 4, 4, 4, 7, 3, 2, 4, 3, 5, 4, 7, 8, 5, 3, 3, 3, 5, 5, 5, 6, 4, 3, 6, 7, 8, 7, 5, 7, 4, 2, 7, 9, 10, 4, 5, 7, 3, 3, 9, 10, 8, 5, 4, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n <= 6 * 10^7, except for a(23) = 0, all a(n) > 0. First occurrence of k beginning with 0: 23, 7, 1, 2, 9, 10, 18, 45, 53, 73, 74, 101, 125, 146, 165, 197, ..., . - Robert G. Wilson v, Jan 14 2018 LINKS W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173. Eric Weisstein's World of Mathematics, Waring's Problem EXAMPLE 2 = 0^2 + 0^2 + 1^3 + 1^3 = 0^2 + 1^2 + 0^3 + 1^3 = 1^2 + 1^2 + 0^3 + 0^3, a(2) = 3. 10 = 0^2 + 1^2 + 1^3 + 2^3 = 0^2 + 3^2 + 0^3 + 1^3 = 1^2 + 1^2 + 0^3 + 2^3 = 1^2 + 3^2 + 0^3 + 0^3 = 2^2 + 2^2 + 1^3 + 1^3, a(10) = 5. MATHEMATICA a[n_] := Sum[If[x^2 + y^2 + z^3 + u^3 == n, 1, 0], {x, 0, n^(1/2)}, {y, x, (n - x^2)^(1/2)}, {z, 0, (n - x^2 - y^2)^(1/3)}, {u, z, (n - x^2 - y^2 - z^3)^(1/3)}]; Table[a[n], {n, 0, 86}] CROSSREFS Cf. A000164, A002635, A022552, A274274. Sequence in context: A300139 A300666 A120881 * A031217 A064131 A111497 Adjacent sequences:  A297927 A297928 A297929 * A297931 A297932 A297933 KEYWORD nonn AUTHOR XU Pingya, Jan 08 2018 STATUS approved

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Last modified October 15 13:38 EDT 2019. Contains 328030 sequences. (Running on oeis4.)