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A295218 Number of partitions of 2*n-1 into four squares.

%I A295218 #19 May 29 2022 18:06:59
%S A295218 1,1,1,1,2,1,2,1,2,2,2,1,3,3,2,2,3,2,3,2,3,3,4,2,4,3,3,3,4,3,4,4,4,4,
%T A295218 4,2,5,5,4,3,6,4,5,4,5,5,5,3,6,6,5,5,6,4,5,5,5,6,8,4,6,6,7,5,7,5,7,7,
%U A295218 6,6,6,5,8,8,6,5,10,6,8,6,7,7,8,5,8,10,7,8,8,6,8,7,9,9,11,5,8,10,7,7
%N A295218 Number of partitions of 2*n-1 into four squares.
%C A295218 This is a bisection of A002635.
%C A295218 While A002635 contains each positive integer infinitely often, here a number can appear only finitely many times.
%C A295218 By the Jacobi theorem, a(n) >= A000203(n)/48 >= (1+n)/48, which implies the previous comment. - _Robert Israel_, Nov 21 2017
%H A295218 Robert Israel, <a href="/A295218/b295218.txt">Table of n, a(n) for n = 1..10000</a>
%H A295218 Wikipedia, <a href="https://en.wikipedia.org/wiki/Jacobi%27s_four-square_theorem"> Jacobi four square theorem</a>
%p A295218 N:= 100: # to get a(1)...a(N)
%p A295218 V:= Array(0..2*N-1):
%p A295218 for a from 0 while 4*a^2 <= 2*N-1 do
%p A295218   for b from a while a^2 + 3*b^2 <= 2*N-1 do
%p A295218      for c from b while a^2 + b^2 + 2*c^2 <= 2*N-1 do
%p A295218        for d from c while a^2 + b^2 + c^2 + d^2 <= 2*N-1 do
%p A295218          t:= a^2 + b^2 + c^2 + d^2;
%p A295218          V[t]:= V[t]+1
%p A295218 od od od od:
%p A295218 seq(V[2*i-1],i=1..N); # _Robert Israel_, Nov 21 2017
%Y A295218 Cf. A002635, A295159.
%K A295218 nonn
%O A295218 1,5
%A A295218 _Franklin T. Adams-Watters_, Nov 17 2017