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%I #20 Feb 10 2017 21:10:27
%S 1,5,10,10,5,6,20,30,20,5,10,30,35,30,30,30,25,30,60,60,25,5,35,80,70,
%T 51,35,50,80,90,80,30,35,60,80,95,90,90,50,75,140,140,85,20,70,120,
%U 130,120,95,115,100,115,140,155,110,40,80,200,230,140,81,120,200,190,180,120,80,100,160,240,200,155,120,140,245,260,230
%N Expansion of (Sum_{k>=0} x^(k*(3*k-1)/2))^5.
%C Number of ways to write n as an ordered sum of 5 pentagonal numbers (A000326).
%C a(n) > 0 for all n >= 0.
%C Every number is the sum of at most 5 pentagonal numbers.
%C Every number is the sum of at most k k-gonal numbers (Fermat's polygonal number theorem).
%H Ilya Gutkovskiy, <a href="/A280718/a280718.pdf">Extended graphical example</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F G.f.: (Sum_{k>=0} x^(k*(3*k-1)/2))^5.
%e a(5) = 6 because we have:
%e [5, 0, 0, 0, 0]
%e [0, 5, 0, 0, 0]
%e [0, 0, 5, 0, 0]
%e [0, 0, 0, 5, 0]
%e [0, 0, 0, 0, 5]
%e [1, 1, 1, 1, 1]
%t nmax = 76; CoefficientList[Series[Sum[x^(k (3 k - 1)/2), {k, 0, nmax}]^5, {x, 0, nmax}], x]
%Y Cf. A000326, A003679, A008439, A038671, A280719, A282248.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Feb 10 2017
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