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A254229 Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566). 3

%I

%S 1,46,207,14652,66493,4717738,21410379,1519096824,6894075385,

%T 489144459430,2219870863431,157502996839476,714791523949237,

%U 50715475837851682,230160650840790723,16330225716791401968,74111014779210663409,5258281965330993581854

%N Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566).

%C Also positive integers y in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of x being A254228.

%H Colin Barker, <a href="/A254229/b254229.txt">Table of n, a(n) for n = 1..797</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).

%F a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

%F G.f.: x*(45*x^3+161*x^2-45*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).

%e 46 is in the sequence because the 46th centered square number is 4141, which is also the 41st heptagonal number.

%o (PARI) Vec(x*(45*x^3+161*x^2-45*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))

%Y Cf. A000566, A001844, A254228, A254230.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 27 2015

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)