A020566 Expansion of 1/((1-5x)(1-9x)(1-12x)).

1, 26, 463, 7040, 98461, 1310486, 16902043, 213488540, 2658229321, 32768006546, 401049136423, 4883135986040, 59232793113781, 716511189600206, 8649599428831603, 104258410046219540, 1255270025244687841, 15100763008086187466, 181546864258080915583

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (26,-213,540).

Formula

a(n) = 25*5^n/28 -27*9^n/4 +48*12^n/7. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=26, a(2)=463; for n>2, a(n) = 26*a(n-1) -213*a(n-2) +540*a(n-3). - Vincenzo Librandi, Jul 04 2013

a(n) = 21*a(n-1) -108*a(n-2) +5^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 9 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 04 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-9*x)*(1-12*x)))); /* or */ I:=[1, 26, 463]; [n le 3 select I[n] else 26*Self(n-1)-213*Self(n-2)+540*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A158427 A158428 A158425 * A021724 A019747 A163740

Adjacent sequences: A020563 A020564 A020565 * A020567 A020568 A020569

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved