A019854 Expansion of 1/((1-5x)(1-6x)(1-11x)).

1, 22, 333, 4334, 52325, 606606, 6874477, 76908238, 854115189, 9445967630, 104219612861, 1148348383182, 12643672205893, 139152654913294, 1531118871452685, 16844976107996366, 185310900907951637, 2038517655246870798, 22424284493969261149, 246670690224670294990

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-151,330).

Formula

G.f.: 1/((1-5*x)*(1-6*x)*(1-11*x)).

a(n) = 25*5^n/6 -36*6^n/5 +121*11^n/30. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=22, a(2)=333; for n>2, a(n) = 22*a(n-1) -151*a(n-2) +330*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n)= 17*a(n-1) -66*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [22, -151, 330][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{22, -151, 330}, {1, 22, 333}, 30] (* Harvey P. Dale, Nov 17 2014 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-11*x)))); /* or */ I:=[1, 22, 333]; [n le 3 select I[n] else 22*Self(n-1)-151*Self(n-2)+330*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A021614 A258006 A309654 * A025936 A369132 A158849

Adjacent sequences: A019851 A019852 A019853 * A019855 A019856 A019857

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved