A020971 Expansion of 1/((1-7*x)*(1-9*x)*(1-11*x)).

1, 27, 490, 7470, 103291, 1343097, 16753780, 202932540, 2405791381, 28065859767, 323426323870, 3691983687210, 41834308968271, 471276683342037, 5284615302054760, 59040661951743480, 657669557062017961

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..957 (terms 0..133 from Charles R Greathouse IV)

Index entries for linear recurrences with constant coefficients, signature (27,-239,693).

Formula

a(n) = 27*a(n-1) - 239*a(n-2) + 693*a(n-3), n>=3. - Vincenzo Librandi, Mar 15 2011

a(n) = 20*a(n-1) - 99*a(n-2) + 7^n, a(0)=1, a(1)=27. - Vincenzo Librandi, Mar 15 2011

a(n) = (7^(n+2)-2*9^(n+2)+11^(n+2))/8. - Bruno Berselli, Mar 15 2011

Mathematica

CoefficientList[Series[1/((1-7x)(1-9x)(1-11x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{27, -239, 693}, {1, 27, 490}, 20] (* Harvey P. Dale, Oct 31 2017 *)

Prog

(PARI) Vec(1/((1-7*x)*(1-9*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(PARI) a(n)=n+=2; (7^n-2*9^n+11^n)/8 \\ Charles R Greathouse IV, Apr 01 2016
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-9*x)*(1-11*x)))); // G. C. Greubel, May 31 2018

Crossrefs

Sequence in context: A025982 A042408 A023946 * A023772 A020726 A020969

Adjacent sequences: A020968 A020969 A020970 * A020972 A020973 A020974

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved