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

Author

Colin Barker, Jan 19 2015

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A000567, A005891, A253921, A253922.

Programs

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

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 *)

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))

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)).