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A331918 Number of compositions (ordered partitions) of n into distinct odd squares.

%I A331918 #9 Feb 03 2020 15:03:48
%S A331918 1,1,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,
%T A331918 2,6,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,2,6,0,0,0,0,0,0,0,0,
%U A331918 0,0,0,0,0,0,2,6,0,0,0,0,0,1,2,6,24,0,0,0,0,0,2
%N A331918 Number of compositions (ordered partitions) of n into distinct odd squares.
%H A331918 Robert Israel, <a href="/A331918/b331918.txt">Table of n, a(n) for n = 0..10000</a>
%H A331918 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A331918 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A331918 a(35) = 6 because we have [25, 9, 1], [25, 1, 9], [9, 25, 1], [9, 1, 25], [1, 25, 9] and [1, 9, 25].
%p A331918 N:= 200: # for a(0)..a(N)
%p A331918 G:= mul(1+t*x^(i^2),i=1..floor(sqrt(N)),2):
%p A331918 F:= proc(n) local R, k, v;
%p A331918   R:= coeff(G,x,n);
%p A331918   add(k!*coeff(R,t,k),k=1..degree(R,t))
%p A331918 end proc:
%p A331918 F(0):= 1:
%p A331918 map(F, [$0..N]); # _Robert Israel_, Feb 03 2020
%Y A331918 Cf. A006456, A016754, A167661, A167700, A280863, A331844.
%K A331918 nonn,look
%O A331918 0,11
%A A331918 _Ilya Gutkovskiy_, Feb 01 2020