A018069 Expansion of 1/((1-3x)(1-8x)(1-10x)).

1, 21, 307, 3873, 45235, 504633, 5465323, 58007361, 606913219, 6283868745, 64556638939, 659310178449, 6703052628403, 67910134629657, 686138217844555, 6917677165178337, 69627131588692387, 699874195511336169

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-134,240).

Formula

a(0)=1, a(1)=21, a(2)=307; for n>2, a(n) = 21*a(n-1) -134*a(n-2) +240*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 18*a(n-1) -80*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (5*10^(n+2) - 7*8^(n+2) + 2*3^(n+2))/70. [Yahia Kahloune, Jul 06 2013]

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 8 x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{21, -134, 240}, {1, 21, 307}, 20] (* Harvey P. Dale, Jul 02 2023 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-8*x)*(1-10*x)))); /* or */ I:=[1, 21, 307]; [n le 3 select I[n] else 21*Self(n-1)-134*Self(n-2)+240*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A081553 A021524 A021268 * A019488 A025929 A021244

Adjacent sequences: A018066 A018067 A018068 * A018070 A018071 A018072

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved