A254138 Pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).

1, 7957, 1185037, 10596309577, 1578130224697, 14111253811878301, 2101618114050816901, 18792154258821103289617, 2798754265133491448134897, 25025774916617575492416996517, 3727140237435880812247465267837, 33327174817289665775049786996211801

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..327

Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).

Formula

a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+7956*x^3-154634*x^2+7956*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).

Example

7957 is in the sequence because it is the 73rd pentagonal number and the 52nd centered hexagonal number.

Mathematica

LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {1, 7957, 1185037, 10596309577, 1578130224697}, 20] (* Harvey P. Dale, Sep 26 2023 *)

Prog

(PARI) Vec(-x*(x^4+7956*x^3-154634*x^2+7956*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A003215, A254136, A254137.

Sequence in context: A316907 A293623 A316908 * A157660 A236786 A252190

Adjacent sequences: A254135 A254136 A254137 * A254139 A254140 A254141

Keyword

nonn,easy

Author

Colin Barker, Jan 26 2015

Status

approved