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Number of compositions (ordered partitions) of n into distinct odd squares.
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%I #9 Feb 03 2020 15:03:48

%S 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 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 0,0,0,0,0,0,2,6,0,0,0,0,0,1,2,6,24,0,0,0,0,0,2

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

%H Robert Israel, <a href="/A331918/b331918.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e 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 N:= 200: # for a(0)..a(N)

%p G:= mul(1+t*x^(i^2),i=1..floor(sqrt(N)),2):

%p F:= proc(n) local R, k, v;

%p R:= coeff(G,x,n);

%p add(k!*coeff(R,t,k),k=1..degree(R,t))

%p end proc:

%p F(0):= 1:

%p map(F, [$0..N]); # _Robert Israel_, Feb 03 2020

%Y Cf. A006456, A016754, A167661, A167700, A280863, A331844.

%K nonn,look

%O 0,11

%A _Ilya Gutkovskiy_, Feb 01 2020