A253921 Indices of octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).

1, 51, 271, 24421, 130461, 11770711, 62881771, 5673458121, 30308883001, 2734595043451, 14608818724551, 1318069137485101, 7041420316350421, 635306589672775071, 3393949983662178211, 306216458153140098961, 1635876850704853547121, 147595697523223854923971

Offset: 1

Author

Colin Barker, Jan 19 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of y being A253922.

Examples

			51 is in the sequence because the 51st octagonal number is 7701, which is also the 56th centered pentagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..745
• Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

Crossrefs

Cf. A000567, A005891, A253922, A253923.

Programs

Magma

I:=[1,51,271,24421,130461]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

Mathematica

CoefficientList[Series[(x^4 + 50 x^3 - 262 x^2 + 50 x + 1)/((1 - x) (x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)

PARI

Vec(-x*(x^4+50*x^3-262*x^2+50*x+1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+50*x^3-262*x^2+50*x+1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).