A254136 Indices of pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).

1, 73, 889, 84049, 1025713, 96992281, 1183671721, 111929008033, 1365956140129, 129165978277609, 1576312202036953, 149057427003352561, 1819062915194503441, 172012141595890577593, 2099197027822254933769, 198501862344230723189569, 2422471551043966999065793

Offset

1,2

Comments

Also positive integers x in the solutions to 3*x^2 - 6*y^2 - x + 6*y - 2 = 0, the corresponding values of y being A254137.

Links

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+72*x^3-338*x^2+72*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

73 is in the sequence because the 73rd pentagonal number is 7957, which is also the 52nd centered hexagonal number.

Mathematica

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 73, 889, 84049, 1025713}, 20] (* Harvey P. Dale, Mar 24 2024 *)

Prog

(PARI) Vec(-x*(x^4+72*x^3-338*x^2+72*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A003215, A254137, A254138.

Sequence in context: A197341 A104907 A296024 * A123811 A057522 A320205

Adjacent sequences: A254133 A254134 A254135 * A254137 A254138 A254139

Keyword

nonn,easy

Author

Colin Barker, Jan 26 2015

Status

approved