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Indices of centered square numbers (A001844) which are also centered heptagonal numbers (A069099).
3

%I #10 Jun 13 2015 00:55:21

%S 1,21,148,5208,37465,1322685,9515836,335956656,2416984753,85331667813,

%T 613904611300,21673907667720,155929354285321,5505087215932941,

%U 39605442083860108,1398270478939299168,10059626359946181985,355155196563366055605,2555105489984246363956

%N Indices of centered square numbers (A001844) which are also centered heptagonal numbers (A069099).

%C Also positive integers x in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of y being A253460.

%H Colin Barker, <a href="/A253459/b253459.txt">Table of n, a(n) for n = 1..832</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,254,-254,-1,1).

%F a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5).

%F G.f.: x*(20*x^3+127*x^2-20*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).

%e 21 is in the sequence because the 21st centered square number is 841, which is also the 16th centered heptagonal number.

%o (PARI) Vec(x*(20*x^3+127*x^2-20*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

%Y Cf. A001844, A069099, A253460, A253599.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 01 2015