cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A175368 Number of integer 4-tuples (x,y,z,u) satisfying |x|^3 + |y|^3 + |z|^3 + |u|^3 = n, -n <= x,y,z,u <= n.

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%I A175368 #13 Aug 26 2021 17:33:04
%S A175368 1,8,24,32,16,0,0,0,8,48,96,64,0,0,0,0,24,96,96,0,0,0,0,0,32,64,0,8,
%T A175368 48,96,64,0,16,0,0,48,192,192,0,0,0,0,0,96,192,0,0,0,0,0,0,64,0,0,24,
%U A175368 96,96,0,0,0,0,0,96,192,8,48,96,64,0,0,96,0,48,192,192,0,0,0,0,0,96,224,64,0
%N A175368 Number of integer 4-tuples (x,y,z,u) satisfying |x|^3 + |y|^3 + |z|^3 + |u|^3 = n, -n <= x,y,z,u <= n.
%C A175368 A variant of A000118 with cubes instead of squares.
%H A175368 Daniel Suteu, <a href="/A175368/b175368.txt">Table of n, a(n) for n = 0..10000</a>
%F A175368 Conjectured g.f.: (1 + 2*Sum_{j>=1} x^(j^3))^4.
%F A175368 a(n) = A175365(n) + 2*Sum_{k=1..floor(n^(1/3))} A175365(n - k^3). - _Daniel Suteu_, Aug 15 2021
%e A175368 a(1) = 8 counts (x,y,z,u) = (-1,0,0,0), (0,-1,0,0), (0,0,-1,0), (0,0,0,-1) and 4 more tuples with -1 replaced by +1.
%e A175368 a(2) = 24 counts (x,y,z,u) = (-1,-1,0,0), (-1,0,-1,0), (-1,0,0,-1), (-1,0,0,1) etc, all variants where two of the 4 values are zero and the other two +1 or -1.
%o A175368 (PARI) a(n, k=4) = if(n==0, return(1)); if(k <= 0, return(0)); if(k == 1, return(ispower(n,3))); my(count = 0); for(v = 0, sqrtnint(n, 3), count += (2 - (v == 0))*if(k > 2, a(n - v^3, k-1), if(ispower(n - v^3, 3), 2 - (n - v^3 == 0), 0))); count; \\ _Daniel Suteu_, Aug 15 2021
%Y A175368 Cf. A000118 , A175362, A175365.
%K A175368 nonn
%O A175368 0,2
%A A175368 _R. J. Mathar_, Apr 24 2010