A253923 Octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).

1, 7701, 219781, 1789106881, 51059956641, 415648888795141, 11862351246525781, 96564381140875635681, 2755885166244302532001, 22434030154994860543881301, 640252753580346501593005701, 5211918753572151610134715970401, 148744800214537374776845967930881

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..373

Index entries for linear recurrences with constant coefficients, signature (1,232322,-232322,-1,1).

Formula

a(n) = a(n-1)+232322*a(n-2)-232322*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+7700*x^3-20242*x^2+7700*x+1) / ((x-1)*(x^2-482*x+1)*(x^2+482*x+1)).

Example

7701 is in the sequence because it is the 51st octagonal number and the 56th centered pentagonal number.

Mathematica

CoefficientList[Series[(x^4 + 7700 x^3 - 20242 x^2 + 7700 x + 1) / ((1 - x) (x^2 - 482 x + 1) (x^2 + 482 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)

Prog

(PARI) Vec(-x*(x^4+7700*x^3-20242*x^2+7700*x+1)/((x-1)*(x^2-482*x+1)*(x^2+482*x+1)) + O(x^100))
(Magma) I:=[1, 7701, 219781, 1789106881, 51059956641]; [n le 5 select I[n] else Self(n-1)+232322*Self(n-2)-232322*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

Crossrefs

Cf. A000567, A005891, A253921, A253922.

Sequence in context: A307134 A183974 A234223 * A259832 A366490 A202597

Adjacent sequences: A253920 A253921 A253922 * A253924 A253925 A253926

Keyword

nonn,easy

Author

Colin Barker, Jan 19 2015

Status

approved