A019613 Expansion of 1/((1-4*x)*(1-7*x)*(1-9*x)).

1, 20, 273, 3172, 33809, 342132, 3348241, 32033924, 301669137, 2808831124, 25937190929, 238042888356, 2174659962385, 19797924540596, 179763483454737, 1628947562960068, 14738065844679953, 133185374228264148

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,-127,252).

Formula

a(n) = 16*4^n/15 -49*7^n/6 +81*9^n/10. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=20, a(2)=273; for n>2, a(n) = 20*a(n-1) -127*a(n-2) +252*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 16*a(n-1) -63*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{20, -127, 252}, {1, 20, 273}, 30] (* G. C. Greubel, Aug 24 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-9*x))));     /* or */   I:=[1, 20, 273]; [n le 3 select I[n] else 20*Self(n-1)-127*Self(n-2)+252*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(PARI) x='x+O('x^30); Vec(1/((1-4*x)*(1-7*x)*(1-9*x))) \\ G. C. Greubel, Aug 24 2018

Crossrefs

Sequence in context: A181384 A269009 A307038 * A021514 A121117 A278722

Adjacent sequences: A019610 A019611 A019612 * A019614 A019615 A019616

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved