A017999 Expansion of 1/((1-3x)(1-7x)(1-10x)).

1, 20, 279, 3370, 37841, 407640, 4281739, 44256950, 452652981, 4597133860, 46465625999, 468116448930, 4705386343321, 47223418005680, 473421066847059, 4742518890351310, 47483346499724861, 475240568299871100, 4755255406504488919, 47572502130747596090

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-121,210).

Formula

a(n) = (4*10^(n+2) - 7^(n+3) + 3^(n+3))/84. - Yahia Kahloune, Jun 30 2013

a(0)=1, a(1)=20, a(2)=279; for n>2, a(n) = 20*a(n-1) -121*a(n-2) +210*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 17*a(n-1) -70*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [20, -121, 210][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 - 7 x) (1 - 10 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)*(1-7*x)*(1-10*x)))); /* or */ I:=[1, 20, 279]; [n le 3 select I[n] else 20*Self(n-1)-121*Self(n-2)+210*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

First differences of A021604.

Sequence in context: A018056 A021234 A021474 * A244653 A012836 A028294

Adjacent sequences: A017996 A017997 A017998 * A018000 A018001 A018002

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved