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

Author

Colin Barker, Jan 26 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A000326, A003215, A254137, A254138.

Programs

Mathematica

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

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))

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)).