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%I #12 Jun 14 2016 09:07:13
%S 1,15,70,1596,7645,175491,840826,19302360,92483161,2123084055,
%T 10172306830,233519943636,1118861268085,25685070715851,
%U 123064567182466,2825124258799920,13535983528803121,310737983397275295,1488835123601160790,34178353049441482476
%N Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).
%C Also positive integers x in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of y being A253477.
%H Colin Barker, <a href="/A253476/b253476.txt">Table of n, a(n) for n = 1..980</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,110,-110,-1,1).
%F a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).
%F G.f.: x*(14*x^3+55*x^2-14*x-1) / ((x-1)*(x^4-110*x^2+1)).
%e 15 is in the sequence because the 15th centered triangular number is 316, which is also the 10th centered heptagonal number.
%t LinearRecurrence[{1,110,-110,-1,1},{1,15,70,1596,7645},30] (* _Harvey P. Dale_, Jun 14 2016 *)
%o (PARI) Vec(x*(14*x^3+55*x^2-14*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))
%Y Cf. A005448, A069099, A253477, A253689.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 02 2015
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