cp's OEIS Frontend

A297930 Number of partitions of n into 2 squares and 2 nonnegative cubes.

%I A297930 #26 Feb 16 2025 08:33:53
%S A297930 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,
%T A297930 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,
%U A297930 5,7,4,2,7,9,10,4,5,7,3,3,9,10,8,5,4,7
%N A297930 Number of partitions of n into 2 squares and 2 nonnegative cubes.
%C A297930 For n <= 6 * 10^7, except for a(23) = 0, all a(n) > 0.
%C A297930 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
%H A297930 W. Jagy and I. Kaplansky, <a href="https://projecteuclid.org/euclid.em/1062621075">Sums of Squares, Cubes and Higher Powers</a>, Experimental Mathematics, vol. 4 (1995) pp. 169-173.
%H A297930 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>
%e A297930 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.
%e A297930 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.
%t A297930 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}]
%Y A297930 Cf. A000164, A002635, A022552, A274274.
%K A297930 nonn
%O A297930 0,2
%A A297930 _XU Pingya_, Jan 08 2018