A020448 Expansion of 1/((1-5x)(1-8x)(1-12x)).

1, 25, 429, 6305, 85541, 1108665, 13976989, 173186065, 2122320981, 25822510505, 312717161549, 3775431050625, 45488017644421, 547320192731545, 6579560264282109, 79048497300991985, 949332313236647861

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-196,480).

Formula

G.f.: 1/((1-5*x)*(1-8*x)*(1-12*x)).

a(n) = 25*5^n/21 -16*8^n/3 +36*12^n/7. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=25, a(2)=429; for n>2, a(n) = 25*a(n-1) -196*a(n-2) +480*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 20*a(n-1) -96*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{25, -196, 480}, {1, 25, 429}, 20] (* Harvey P. Dale, Apr 01 2016 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1, 25, 429]; [n le 3 select I[n] else 25*Self(n-1)-196*Self(n-2)+480*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A020577 A021714 A056090 * A203544 A021704 A019742

Adjacent sequences: A020445 A020446 A020447 * A020449 A020450 A020451

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved