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

Author

Roger L. Bagula, Aug 17 2006

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A007482.

Programs

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

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 *)

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

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

Extensions

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

Meaningful name from Joerg Arndt, Dec 26 2022