A020572 Expansion of 1/((1-6x)(1-7x)(1-10x)).

1, 23, 357, 4675, 55781, 628803, 6831637, 72401555, 754291461, 7764923683, 79263766517, 804302170035, 8126850016741, 81868359076163, 822960967286997, 8260021493532115, 82815918789863621, 829686041539878243

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-172,420).

Formula

a(n) = 9*6^n -49*7^n/3 +25*10^n/3. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=23, a(2)=357; for n>2, a(n) = 23*a(n-1) -172*a(n-2) +420*a(n-3). - Vincenzo Librandi, Jul 04 2013

a(n) = 17*a(n-1) -70*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 6 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 04 2013 *)
LinearRecurrence[{23, -172, 420}, {1, 23, 357}, 20] (* Harvey P. Dale, Sep 24 2016 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-10*x)))); /* or */ I:=[1, 23, 357]; [n le 3 select I[n] else 23*Self(n-1)-172*Self(n-2)+420*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A022412 A025946 A118115 * A021884 A101792 A020346

Adjacent sequences: A020569 A020570 A020571 * A020573 A020574 A020575

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved