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%I #9 Oct 13 2015 15:13:06
%S 0,486,701100,1010986002,1457841114072,2102205875506110,
%T 3031379414638696836,4371247013703125331690,6303335162380492089600432,
%U 9089404932905655890078491542,13106915609914793413001095203420,18900163220092199195891689204840386
%N Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the hexagonal number X(m) for some m.
%C Also nonnegative integers x in the solutions to 10*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of y being A252077.
%H Colin Barker, <a href="/A252076/b252076.txt">Table of n, a(n) for n = 1..317</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1443,-1443,1).
%F a(n) = 1443*a(n-1)-1443*a(n-2)+a(n-3).
%F G.f.: 18*x^2*(11*x-27) / ((x-1)*(x^2-1442*x+1)).
%e 486 is in the sequence because H(486)+H(487) = 589761+592192 = 1181953 = X(769).
%t LinearRecurrence[{1443,-1443,1},{0,486,701100},20] (* _Harvey P. Dale_, Oct 13 2015 *)
%o (PARI) concat(0, Vec(18*x^2*(11*x-27)/((x-1)*(x^2-1442*x+1)) + O(x^100)))
%Y Cf. A000384, A000566, A252077.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 13 2014
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