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%I #6 Jun 13 2015 00:55:24
%S 1,13,44,776,2697,48069,167140,2979472,10359953,184679165,642149916,
%T 11447128728,39802934809,709537301941,2467139808212,43979865591584,
%U 152922865174305,2726042129376237,9478750500998668,168970632155735080,587529608196743081
%N Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).
%C Also positive integers y in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of x being A254674.
%H Colin Barker, <a href="/A254675/b254675.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,62,-62,-1,1).
%F a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).
%F G.f.: x*(12*x^3+31*x^2-12*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).
%e 13 is in the sequence because the 13th centered triangular number is 235, which is also the 10th heptagonal number.
%o (PARI) Vec(x*(12*x^3+31*x^2-12*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))
%Y Cf. A000566, A005448, A254674, A254676.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Feb 05 2015
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