A019928 Expansion of 1/((1-5x)(1-7x)(1-8x)).

1, 20, 269, 3040, 31161, 300300, 2775109, 24887960, 218303921, 1882786180, 16026538749, 135010883280, 1127921219881, 9359429537660, 77233958267189, 634411837477000, 5191228487083041, 42342127346986740

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 (20,-131,280).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-8*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 20, 269]; [n le 3 select I[n] else 20*Self(n-1)-131*Self(n-2)+280*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 7 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Formula

a(n) = 25*5^n/6 -49*7^n/2 +64*8^n/3. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=20, a(2)=269; for n>2, a(n) = 20*a(n-1) -131*a(n-2) +280*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 15*a(n-1) -56*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013