A253457 Indices of centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).

1, 14, 351, 9100, 236237, 6133050, 159223051, 4133666264, 107316099801, 2786084928550, 72330892042487, 1877817108176100, 48750913920536101, 1265645944825762514, 32858043651549289251, 853043488995455758000, 22146272670230300418737, 574950045936992355129150

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 6*x + 7*y = 0, the corresponding values of y being A253458.

Examples

			14 is in the sequence because the 14th centered hexagonal number is 547, which is also the 13th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..708
• Index entries for linear recurrences with constant coefficients, signature (27,-27,1).

Crossrefs

Cf. A003215, A069099, A253458, A253546.

Programs

PARI

Vec(x*(13*x-1)/((x-1)*(x^2-26*x+1)) + O(x^100))

Formula

a(n) = 27*a(n-1)-27*a(n-2)+a(n-3).

G.f.: x*(13*x-1) / ((x-1)*(x^2-26*x+1)).

a(n) = sqrt((-2-(13-2*sqrt(42))^n-(13+2*sqrt(42))^n)*(2-(13-2*sqrt(42))^(1+n)-(13+2*sqrt(42))^(1+n)))/(4*sqrt(6)). - Gerry Martens, Jun 04 2015