A017932 Expansion of 1/((1-3x)(1-6x)(1-8x)).

1, 17, 199, 1997, 18487, 163205, 1398223, 11743469, 97300423, 798539093, 6509186047, 52798905341, 426744275959, 3440074001381, 27677315556271, 222358880070413, 1784513217331495, 14309958928401269, 114682790953126495

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-90,144).

Formula

a(0)=1, a(1)=17, a(2)=199; for n>2, a(n) = 17*a(n-1) -90*a(n-2) +144*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 14*a(n-1) -48*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) =(3*8^(n+2) - 5*6^(n+2) + 2*3^(n+2))/30. [Yahia Kahloune, Jul 06 2013]

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [17, -90, 144][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 02 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 17, 199]; [n le 3 select I[n] else 17*Self(n-1)-90*Self(n-2)+144*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A177075 A177076 A196491 * A125429 A244002 A201258

Adjacent sequences: A017929 A017930 A017931 * A017933 A017934 A017935

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved