A016093 Expansion of 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).

1, 41, 1055, 21805, 395871, 6595701, 103397575, 1549123085, 22414242191, 315506452261, 4343673465495, 58723278269565, 781995624847711, 10282227616659221, 133750220517219815, 1723860289008683245

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (41,-626,4216,-10560).

Formula

G.f.: 1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)).

a(n) = -8^(2+n)/3 - 11^(n+3)/3 +25*10^(n+1) +18*12^(n+1). - R. J. Mathar, Mar 14 2011

a(n) = 41*a(n-1) -626*a(n-2) +4216*a(n-3) -10560*a(n-4), n>=4. - Vincenzo Librandi, Mar 18 2011

a(n) = 23*a(n-1) -132*a(n-2) +5*10^n-4*8^n, n>=2. - Vincenzo Librandi, Mar 18 2011

Mathematica

CoefficientList[Series[1 / ((1 - 8 x) (1 - 10 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)

Prog

(PARI) Vec(1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-10*x)*(1-11*x)*(1-12*x)))); /* or */ I:=[1, 41, 1055, 21805]; [n le 4 select I[n] else 41*Self(n-1)-626*Self(n-2)+4216*Self(n-3)-10560*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Jun 24 2013

Crossrefs

Sequence in context: A059762 A368809 A069362 * A358713 A130639 A196744

Adjacent sequences: A016090 A016091 A016092 * A016094 A016095 A016096

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved