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

Author

Colin Barker, Jan 26 2015

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A000326, A003215, A254136, A254137.

Programs

Mathematica

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

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))

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)).