A020343 Expansion of 1/((1-5x)(1-8x)(1-9x)).

1, 22, 327, 4100, 46781, 503202, 5201827, 52278640, 514595961, 4986022382, 47721236927, 452316244380, 4253691236341, 39747202125562, 369442770633627, 3418759065309320, 31519177212527921, 289676122850156742

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,-157,360).

Formula

a(n) = 25*5^n/12 -64*8^n/3 +81*9^n/4. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=22, a(3)=327; for n>2, a(n) = 22*a(n-1) -157*a(n-2) +360*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 17*a(n-1) -72*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-9*x)))); /* or */ I:=[1, 22, 327]; [n le 3 select I[n] else 22*Self(n-1)-157*Self(n-2)+360*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A020571 A021874 A025963 * A025941 A125479 A047868

Adjacent sequences: A020340 A020341 A020342 * A020344 A020345 A020346

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved