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

1,2

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.

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).

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)).

Example

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

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 *)

Prog

(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))
(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

Crossrefs

Cf. A000567, A005891, A253922, A253923.

Sequence in context: A201813 A193250 A204717 * A204956 A243462 A251351

Adjacent sequences: A253918 A253919 A253920 * A253922 A253923 A253924

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2015

Status

approved