A019512 Expansion of 1/((1-4x)(1-7x)(1-8x)).

1, 19, 245, 2675, 26661, 251139, 2278165, 20125075, 174364421, 1488724259, 12567504885, 105148209075, 873459639781, 7213661997379, 59291458568405, 485407880414675, 3960800821356741, 32229188196998499

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-116,224).

Formula

a(n) = (3*8^(n+2)-4*7^(n+2)+4^(n+2))/12. [Yahia Kahloune, May 06 2013]

a(0)=1, a(1)=19, a(2)=245; for n>2, a(n) = 19*a(n-1) -116*a(n-2) +224*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 15*a(n-1) -56*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{19, -116, 224}, {1, 19, 245}, 20] (* Harvey P. Dale, Sep 26 2019 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 19, 245]; [n le 3 select I[n] else 19*Self(n-1)-116*Self(n-2)+224*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jl 03 2013

Crossrefs

Sequence in context: A021772 A019783 A021504 * A025927 A224180 A318194

Adjacent sequences: A019509 A019510 A019511 * A019513 A019514 A019515

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved