A253714 Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).

1, 2857, 45529, 184300369, 2937241777, 11889953986681, 189493215939721, 767068491312421537, 12224965330197902689, 49486656636639609035209, 788681413122894278122297, 3192582165489099245985035761, 50880992673985436128583949841

Offset

1,2

Comments

Also positive integers x in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of y being A253715.

Links

Colin Barker, Table of n, a(n) for n = 1..416

Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).

Formula

a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+2856*x^3-21842*x^2+2856*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).

Example

2857 is in the sequence because the 2857th hexagonal number is 16322041, which is also the 2160th centered heptagonal number.

Prog

(PARI) Vec(-x*(x^4+2856*x^3-21842*x^2+2856*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))

Crossrefs

Cf. A000384, A069099, A253715, A253716.

Sequence in context: A233788 A250637 A067703 * A031603 A236586 A233379

Adjacent sequences: A253711 A253712 A253713 * A253715 A253716 A253717

Keyword

nonn,easy

Author

Colin Barker, Jan 10 2015

Status

approved