A020972 Expansion of 1/((1-7*x)*(1-9*x)*(1-12*x)).

1, 28, 529, 8428, 122257, 1673980, 22067473, 283450636, 3574941073, 44501447452, 548719235857, 6718924954924, 81849587868049, 993294339107644, 12020103854584081, 145151139884150092, 1750035954202640785

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..923

Index entries for linear recurrences with constant coefficients, signature (28,-255,756).

Formula

a(n) = 28*a(n-1) - 255*a(n-2) + 756*a(n-3), n>=3. - Vincenzo Librandi, Mar 15 2011

a(n) = 21*a(n-1) - 108*a(n-2) + 7^n, a(0)=1, a(1)=28. - Vincenzo Librandi, Mar 15 2011

a(n) = (2*12^(n+2) - 5*9^(n+2) + 3*7^(n+2))/30. - Yahia Kahloune, Jun 30 2013

Mathematica

CoefficientList[Series[1/((1-7x)(1-9x)(1-12x)), {x, 0, 50}], x] (* G. C. Greubel, May 31 2018 *)
LinearRecurrence[{28, -255, 756}, {1, 28, 529}, 20] (* Harvey P. Dale, Oct 08 2020 *)

Prog

(PARI) x='x+O('x^50); Vec(1/((1-7*x)*(1-9*x)*(1-12*x))) \\ G. C. Greubel, May 31 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-9*x)*(1-12*x))));  // G. C. Greubel, May 31 2018

Crossrefs

Sequence in context: A020977 A020973 A023947 * A025957 A020758 A022000

Adjacent sequences: A020969 A020970 A020971 * A020973 A020974 A020975

Keyword

nonn

Author

N. J. A. Sloane

Status

approved