login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A018209 Expansion of 1/((1-4x)(1-5x)(1-7x)). 1
1, 16, 173, 1580, 13161, 103656, 787333, 5836420, 42545921, 306538496, 2190403293, 15560186460, 110074899481, 776359376536, 5463959472053, 38396009227700, 269517824177841, 1890370747033776, 13251393837657613 (list; graph; refs; listen; history; text; internal format)
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)))); /* or */ 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: A230510 A238725 A221789 * A021174 A021374 A253343

Adjacent sequences: A018206 A018207 A018208 * A018210 A018211 A018212

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)