cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A218571 Number of partitions p of n such that max(p)-min(p) = 8.

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%I A218571 #13 Sep 11 2017 02:36:14
%S A218571 1,1,3,3,7,8,14,18,28,35,52,65,90,113,152,188,246,302,387,471,591,714,
%T A218571 884,1059,1292,1538,1857,2193,2621,3077,3646,4254,4999,5801,6772,7815,
%U A218571 9062,10409,12002,13719,15733,17909,20438,23169,26318,29722,33623,37833
%N A218571 Number of partitions p of n such that max(p)-min(p) = 8.
%H A218571 Alois P. Heinz, <a href="/A218571/b218571.txt">Table of n, a(n) for n = 10..1000</a>
%H A218571 G. E. Andrews, M. Beck and N. Robbins, <a href="https://arxiv.org/abs/1406.3374">Partitions with fixed differences between largest and smallest parts</a>, arXiv:1406.3374 [math.NT], 2014.
%F A218571 G.f.: Sum_{k>0} x^(2*k+8)/Product_{j=0..8} (1-x^(k+j)).
%F A218571 a(n) = A097364(n,8) = A116685(n,8) = A194621(n,8) - A194621(n,7) = A218510(n) - A218509(n).
%t A218571 terms = 48; offset = 10; max = terms + offset; s[k0_ /; k0 > 0] := Sum[x^(2*k + k0)/Product[ (1 - x^(k + j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x] &; Drop[s[8], offset] (* _Jean-François Alcover_, Sep 11 2017, after _Alois P. Heinz_ *)
%K A218571 nonn
%O A218571 10,3
%A A218571 _Alois P. Heinz_, Nov 02 2012