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Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844).
4

%I #12 Mar 12 2024 13:01:04

%S 1,16,112,3937,28321,999856,7193296,253959361,1827068737,64504677712,

%T 464068265776,16383934179361,117871512438241,4161454776879856,

%U 29938900091047312,1056993129393303937,7604362751613578881,268472093411122320016,1931478200009757988336

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

%C Also positive integers y in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of x being A253459.

%H Colin Barker, <a href="/A253460/b253460.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*(x^4+15*x^3-158*x^2+15*x+1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).

%F a(n) = A105040(n) + 1. - _Michel Marcus_, Mar 12 2024

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

%o (PARI) Vec(-x*(x^4+15*x^3-158*x^2+15*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

%Y Cf. A001844, A069099, A253459, A253599.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 01 2015