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A018209

Expansion of 1/((1-4x)(1-5x)(1-7x)).

1, 16, 173, 1580, 13161, 103656, 787333, 5836420, 42545921, 306538496, 2190403293, 15560186460, 110074899481, 776359376536, 5463959472053, 38396009227700, 269517824177841, 1890370747033776, 13251393837657613

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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,-83,140).

FORMULA

a(n) = 16*4^n/3 -25*5^n/2 +49*7^n/6. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=16, a(2)=173; for n>2, a(n) = 16*a(n-1) -83*a(n-2) +140*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 12*a(n-1) -35*a(n-2) + 4^n. - Vincenzo Librandi, Jul 02 2013

MATHEMATICA

CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)

LinearRecurrence[{16, -83, 140}, {1, 16, 173}, 30] (* Harvey P. Dale, Oct 18 2013 *)

PROG

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-7*x)))); // Vincenzo Librandi, Jul 02 2013

(Magma) I:=[1, 16, 173]; [n le 3 select I[n] else 16*Self(n-1)-83*Self(n-2)+140*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

CROSSREFS

Sequence in context: A238725 A388204 A221789 * A021174 A021374 A253343

Adjacent sequences: A018206 A018207 A018208 * A018210 A018211 A018212

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A018209

⇱ A018209 - OEIS