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%I #20 Jul 10 2021 19:30:10
%S 1,1,3,3,7,8,13,16,24,27,40,46,60,71,92,103,131,149,181,206,247,275,
%T 329,366,424,474,548,601,690,759,858,942,1059,1152,1293,1404,1555,
%U 1690,1869,2013,2218,2390,2614,2812,3066,3282,3574,3820,4131,4415,4769,5071
%N Number of partitions p of n such that max(p)-min(p) = 4.
%H Alois P. Heinz, <a href="/A218567/b218567.txt">Table of n, a(n) for n = 6..1000</a>
%H 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 G.f.: Sum_{k>0} x^(2*k+4)/Product_{j=0..4} (1-x^(k+j)).
%F a(n) = A097364(n,4) = A116685(n,4) = A194621(n,4) - A194621(n,3) = A218506(n) - A117143(n).
%t terms = 52; offset = 6; 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[4], offset] (* _Jean-François Alcover_, Sep 11 2017, after _Alois P. Heinz_ *)
%t Table[Count[IntegerPartitions[n],_?(#[[1]]-#[[-1]]==4&)],{n,6,60}] (* _Harvey P. Dale_, Jul 10 2021 *)
%K nonn
%O 6,3
%A _Alois P. Heinz_, Nov 02 2012
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