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

1,2

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.

Links

Colin Barker, Table of n, a(n) for n = 1..708

Index entries for linear recurrences with constant coefficients, signature (27,-27,1).

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

Example

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

Prog

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

Crossrefs

Cf. A003215, A069099, A253458, A253546.

Sequence in context: A239783 A020143 A161927 * A239784 A113673 A184268

Adjacent sequences: A253454 A253455 A253456 * A253458 A253459 A253460

Keyword

nonn,easy

Author

Colin Barker, Jan 01 2015

Status

approved