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%I #6 Jun 13 2015 00:55:19
%S 90,84515202,79520184374490,74820382437504220002,
%T 70398348194603325406910490,66237665019531059286273761843202,
%U 62322886541476336272141806645338008090,58639479301035764180766150529698967373864802,55173768795323625559613033164820557197489306307290
%N Numbers n such that the pentagonal number P(n) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m.
%C Also nonnegative integers y in the solutions to 18*x^2-3*y^2+24*x+y+18 = 0, the corresponding values of x being A252092.
%H Colin Barker, <a href="/A252093/b252093.txt">Table of n, a(n) for n = 1..168</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (940899,-940899,1).
%F a(n) = 940899*a(n-1)-940899*a(n-2)+a(n-3).
%F G.f.: -18*x*(489*x^2-9206*x+5) / ((x-1)*(x^2-940898*x+1)).
%e 90 is in the sequence because P(90) = 12105 = 3816+4033+4256 = N(36)+N(37)+N(38).
%o (PARI) Vec(-18*x*(489*x^2-9206*x+5)/((x-1)*(x^2-940898*x+1)) + O(x^100))
%Y Cf. A000326, A000567, A252092.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Dec 14 2014
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