A253460 Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844).

1, 16, 112, 3937, 28321, 999856, 7193296, 253959361, 1827068737, 64504677712, 464068265776, 16383934179361, 117871512438241, 4161454776879856, 29938900091047312, 1056993129393303937, 7604362751613578881, 268472093411122320016, 1931478200009757988336

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

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.

Examples

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

Links

• Colin Barker, Table of n, a(n) for n = 1..832
• Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

Crossrefs

Cf. A001844, A069099, A253459, A253599.

Programs

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))

Formula

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

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)).

a(n) = A105040(n) + 1. - Michel Marcus, Mar 12 2024