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%I #6 Jun 13 2015 00:55:19
%S 1,769,1108537,1598509225,2305049193553,3323879338593841,
%T 4793031701203124809,6911548389255567380377,9966447984274826959378465,
%U 14371611081775911219856365793,20723853213472879704205920094681,29883781962216810757553716920163849
%N Numbers n such that the hexagonal number X(n) is equal to the sum of the heptagonal number H(m) and H(m+1) for some m.
%C Also nonnegative integers y in the solutions to 10*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of x being A252076.
%H Colin Barker, <a href="/A252077/b252077.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.: -x*(313*x^2-674*x+1) / ((x-1)*(x^2-1442*x+1)).
%e 769 is in the sequence because X(769) = 1181953 = 589761+592192 = H(486)+H(487).
%o (PARI) Vec(-x*(313*x^2-674*x+1)/((x-1)*(x^2-1442*x+1)) + O(x^100))
%Y Cf. A000384, A000566, A252076.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 13 2014
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