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Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).
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%I #11 Aug 31 2021 13:41:32

%S 1,2,16,43,407,1108,10558,28757,274093,746566,7115852,19381951,

%T 184738051,503184152,4796073466,13063405993,124513172057,339145371658,

%U 3232546400008,8804716257107,83921693228143,228583477313116,2178731477531702,5934365693883901

%N Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).

%C Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of y being A254856.

%H Colin Barker, <a href="/A254855/b254855.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 (1,26,-26,-1,1).

%F a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+x^3-12*x^2+x+1) / ((x-1)*(x^4-26*x^2+1)).

%e 16 is in the sequence because the 16th octagonal number is 736, which is also the 15th centered heptagonal number.

%t LinearRecurrence[{1,26,-26,-1,1},{1,2,16,43,407},30] (* _Harvey P. Dale_, Aug 31 2021 *)

%o (PARI) Vec(-x*(x^4+x^3-12*x^2+x+1)/((x-1)*(x^4-26*x^2+1)) + O(x^100))

%Y Cf. A000567, A069099, A254856, A254857.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Feb 08 2015