A017931 Expansion of 1/((1-3x)(1-6x)(1-7x)).

1, 16, 175, 1630, 13921, 112756, 881875, 6730810, 50468341, 373414096, 2734771975, 19868820790, 143434778761, 1030163245036, 7367866260475, 52515419443570, 373250112873181, 2646603979861576, 18729347384947375

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (16,-81,126).

Formula

a(0)=1, a(1)=16, a(2)=175; for n>2, a(n) = 16*a(n-1) -81*a(n-2) +126*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 13*a(n-1) -42*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (3*7^(n+2) - 4*6^n+2) + 3^(n+2))/12. [Yahia Kahloune, Jul 06 2013]

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [16, -81, 126][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 - 7 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)*(1-7*x)))); /* or */ I:=[1, 16, 175]; [n le 3 select I[n] else 16*Self(n-1)-81*Self(n-2)+126*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A253343 A215687 A187720 * A021129 A268869 A268459

Adjacent sequences: A017928 A017929 A017930 * A017932 A017933 A017934

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved