A019671 Expansion of 1/((1-4x)(1-8x)(1-10x)).

1, 22, 332, 4280, 50736, 571872, 6238912, 66567040, 699159296, 7259766272, 74744097792, 764616652800, 7783588704256, 78935331561472, 798149140201472, 8051859072450560, 81081536382959616, 815318946277097472

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,-152,320).

Formula

a(n)= 2*4^n/3 -8^(n+1)+25*10^n/3 . - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=22, a(2)=332; for n>2, a(n) = 22*a(n-1) -152*a(n-2) +320*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -80*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{22, -152, 320}, {1, 22, 332}, 20] (* Harvey P. Dale, Aug 28 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-8*x)*(1-10*x)))); /* or */ I:=[1, 22, 332]; [n le 3 select I[n] else 22*Self(n-1)-152*Self(n-2)+320*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A019958 A021644 A021834 * A021614 A258006 A309654

Adjacent sequences: A019668 A019669 A019670 * A019672 A019673 A019674

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved