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%I #8 Apr 20 2017 03:22:12
%S 1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,
%T 0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,0,0,0,
%U 1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,2,2,0,0,0,0,0,1
%N Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)+1)).
%C Number of partitions of n into distinct centered hexagonal numbers (A003215).
%H G. C. Greubel, <a href="/A281084/b281084.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexNumber.html">Hex Number</a>
%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)+1)).
%e a(98) = 2 because we have [91, 7] and [61, 37].
%t nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1) + 1), {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A003215, A279279, A280953, A281081, A281082, A281083.
%K nonn
%O 0,99
%A _Ilya Gutkovskiy_, Jan 14 2017
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