cp's OEIS Frontend

A385860 a(n) is the number of distinct multisets of sides of quadrilaterals with perimeter n, where all four sides are squares.

%I A385860 #14 Jul 23 2025 16:17:13
%S A385860 0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,1,
%T A385860 1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,3,0,1,1,0,1,2,1,1,1,0,1,1,0,1,1,
%U A385860 1,0,1,0,0,1,2,1,1,2,1,2,1,1,2,0,2,1,1,1
%N A385860 a(n) is the number of distinct multisets of sides of quadrilaterals with perimeter n, where all four sides are squares.
%C A385860 a(n) is the number of partitions of n into 4 nonzero squares < n/2.
%H A385860 Felix Huber, <a href="/A385860/b385860.txt">Table of n, a(n) for n = 0..10000</a>
%F A385860 a(n) <= A025428(n).
%e A385860 The a(51) = 1 multiset is [1, 9, 16, 25].
%e A385860 The a(52) = 3 multisets are [1, 1, 25, 25], [4, 16, 16, 16] and [9, 9, 9, 25].
%p A385860 # After Alois P. Heinz (A025428)
%p A385860 b:=proc(n,i,t)
%p A385860     option remember;
%p A385860     `if`(n=0,`if`(t=0,1,0),`if`(i<1 or t<1, 0, b(n,i-1,t)+`if`(i^2>n,0,b(n-i^2,i,t-1))))
%p A385860     end:
%p A385860 A385860:=n->b(n,floor(sqrt((n-1)/2)),4):
%p A385860 seq(A385860(n),n=0..87);
%Y A385860 Cf. A000290, A000414, A000534, A025428, A062890, A385736.
%K A385860 nonn
%O A385860 0,53
%A A385860 _Felix Huber_, Jul 22 2025