A018090 Expansion of 1/((1-3*x)*(1-9*x)*(1-10*x)).

1, 22, 337, 4450, 54301, 631462, 7111417, 78287530, 847442101, 9055541902, 95785566097, 1004927161810, 10472915657101, 108541954516342, 1119734731454377, 11506184005511290, 117841370316867301, 1203429475653602782, 12259436709287816257, 124620644668806519970, 1264442944874907200701

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,-147,270).

Formula

a(0)=1, a(1)=22, a(2)=337; for n>2 a(n) = 22*a(n-1) -147*a(n-2) +270*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 19*a(n-1) -90*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (6*10^(n+2) - 7*9^(n+2) + 3^(n+2))/42. - Yahia Kahloune, Jul 06 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{22, -147, 270}, {1, 22, 337}, 20] (* Harvey P. Dale, Nov 11 2024 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-9*x)*(1-10*x)))); // Vincenzo Librandi, Jul 02 2013
(Magma) I:=[1, 22, 337]; [n le 3 select I[n] else 22*Self(n-1)-147*Self(n-2)+270*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A021794 A348134 A223812 * A021274 A021534 A018070

Adjacent sequences: A018087 A018088 A018089 * A018091 A018092 A018093

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved