A254654 Pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).

1, 22, 11572, 265651, 139997551, 3213845272, 1693690359922, 38881099834501, 20490265834338301, 470383542583947322, 247891234370134405072, 5690700059299494866551, 2998988132919620198222251, 68846088847021746311586172, 36281758184170330787958387022

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..490

Index entries for linear recurrences with constant coefficients, signature (1,12098,-12098,-1,1).

Formula

a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+21*x^3-548*x^2+21*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)).

Example

22 is in the sequence because it is the 4th pentagonal number and the 3rd centered heptagonal number.

Mathematica

CoefficientList[Series[(x^4 + 21*x^3 - 548*x^2 + 21*x + 1)/((1 - x)*(x^2 - 110*x + 1)*(x^2 + 110*x + 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 19 2017 *)

Prog

(PARI) Vec(-x*(x^4+21*x^3-548*x^2+21*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100))
(Magma) I:=[1, 22, 11572, 265651, 139997551]; [n le 5 select I[n] else Self(n-1)+12098*Self(n-2)-12098*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Jan 20 2017

Crossrefs

Cf. A000326, A069099, A254652, A254653.

Sequence in context: A013727 A370314 A229346 * A028692 A127486 A232847

Adjacent sequences: A254651 A254652 A254653 * A254655 A254656 A254657

Keyword

nonn,easy

Author

Colin Barker, Feb 04 2015

Status

approved