A120723 Expansion of x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)).

1, 11, 63, 247, 887, 3207, 11383, 40679, 144663, 515719, 1835831, 6540327, 23289943, 82955975, 295436919, 1052244583, 3747563927, 13347268359, 47536758199, 169305160871, 602988299991, 2147576619847, 7648703663351

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,7,-4,-4).

Formula

G.f.: x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)). - Colin Barker, Apr 04 2012

a(n) = 12*[n=0] - 23/3 + (-2)^n/6 - (9/2)*(A007482(n) - 5*A007482(n- 1)). - G. C. Greubel, Jul 20 2023

Mathematica

CoefficientList[Series[(1+3x)*(1 +6x +16x^2)/((1-x)*(1+2x)*(1-3x-2x^2)), {x, 0, 50}], x] (* Bruno Berselli, Apr 04 2012 *)
LinearRecurrence[{2, 7, -4, -4}, {1, 11, 63, 247}, 40] (* G. C. Greubel, Jul 20 2023 *)

Prog

(Magma) I:=[1, 11, 63, 247]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) -4*Self(n-3) -4*Self(n-4): n in [1..40]]; // G. C. Greubel, Jul 20 2023
(SageMath)
A007482=BinaryRecurrenceSequence(3, 2, 1, 3)
def A120723(n): return 12*int(n==0) - (1/6)*(46 - (-2)^n + 27*(A007482(n) - 5*A007482(n-1)))
[A120723(n) for n in range(41)] # G. C. Greubel, Jul 20 2023

Crossrefs

Cf. A007482.

Sequence in context: A162946 A301610 A298046 * A053367 A163706 A180763

Adjacent sequences: A120720 A120721 A120722 * A120724 A120725 A120726

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 17 2006

Extensions

Edited by N. J. A. Sloane, Jun 15 2007

Meaningful name from Joerg Arndt, Dec 26 2022

Status

approved