A019490 Expansion of 1/((1-4*x)*(1-6*x)*(1-12*x)).

1, 22, 340, 4600, 58576, 724192, 8822080, 106672000, 1284971776, 15449370112, 185571742720, 2227940915200, 26741787774976, 320940501164032, 3851520569589760, 46219655242547200, 554644317650354176

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (22,-144,288).

Formula

a(n) = 4^n -3*6^n +3*12^n. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=22, a(2)=340; for n>2, a(n) = 22*a(n-1) -144*a(n-2) +288*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -72*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1/((1-4x)(1-6x)(1-12x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-12*x))));  /* or */  I:=[1, 22, 340]; [n le 3 select I[n] else 22*Self(n-1)-144*Self(n-2)+288*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(PARI) my(x='x+O('x^20)); Vec(1/((1-4*x)*(1-6*x)*(1-12*x))) \\ G. C. Greubel, Apr 27 2019
(Sage) (1/((1-4*x)*(1-6*x)*(1-12*x))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019
(GAP) List([0..20], n-> 2^n*(2^n -3^(n+1) +3*6^n)) # G. C. Greubel, Apr 27 2019

Crossrefs

Sequence in context: A021534 A018070 A332873 * A021254 A231647 A083449

Adjacent sequences: A019487 A019488 A019489 * A019491 A019492 A019493

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved