A019443 Expansion of 1/((1-4x)(1-6x)(1-9x)).

1, 19, 247, 2743, 28063, 273847, 2596399, 24174631, 222479455, 2032023895, 18467516431, 167287650439, 1512085646527, 13647818683063, 123064923768943, 1108992721390567, 9989389232302879, 89955248709321751

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (19,-114,216).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-9*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 19, 247]; [n le 3 select I[n] else 19*Self(n-1)-114*Self(n-2)+216*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 9 x)),{x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{19,-114,216},{1,19,247},30] (* Harvey P. Dale, Oct 04 2019 *)

Formula

a(n) = 8*4^n/5 -6*6^n +27*9^n/5. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=19, a(2)=247; for n>2, a(n) = 19*a(n-1) -114*a(n-2) +216*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 15*a(n-1) -54*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013