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%I #15 Jun 13 2015 00:55:21
%S 1,14,351,9100,236237,6133050,159223051,4133666264,107316099801,
%T 2786084928550,72330892042487,1877817108176100,48750913920536101,
%U 1265645944825762514,32858043651549289251,853043488995455758000,22146272670230300418737,574950045936992355129150
%N Indices of centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
%C Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 6*x + 7*y = 0, the corresponding values of y being A253458.
%H Colin Barker, <a href="/A253457/b253457.txt">Table of n, a(n) for n = 1..708</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-27,1).
%F a(n) = 27*a(n-1)-27*a(n-2)+a(n-3).
%F G.f.: x*(13*x-1) / ((x-1)*(x^2-26*x+1)).
%F a(n) = sqrt((-2-(13-2*sqrt(42))^n-(13+2*sqrt(42))^n)*(2-(13-2*sqrt(42))^(1+n)-(13+2*sqrt(42))^(1+n)))/(4*sqrt(6)). - _Gerry Martens_, Jun 04 2015
%e 14 is in the sequence because the 14th centered hexagonal number is 547, which is also the 13th centered heptagonal number.
%o (PARI) Vec(x*(13*x-1)/((x-1)*(x^2-26*x+1)) + O(x^100))
%Y Cf. A003215, A069099, A253458, A253546.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 01 2015