A016218 Expansion of 1/((1-x)*(1-4*x)*(1-5*x)).

1, 10, 71, 440, 2541, 14070, 75811, 400900, 2091881, 10808930, 55442751, 282806160, 1436400421, 7271480590, 36715316891, 185008240220, 930767824161, 4676745613050, 23475354034231, 117743274047080, 590182385739101, 2956775990710310, 14807336201610771

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

Crossrefs

Cf. A016208, A000392, A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A016256.

Programs

PARI

Vec(1/((1-x)*(1-4*x)*(1-5*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Formula

From Vincenzo Librandi, Feb 10 2011: (Start)

a(n) = a(n-1) + 5^(n+1) - 4^(n+1), n >= 1.

a(n) = 9*a(n-1) - 20*a(n-2) + 1, n >= 2. (End)

a(n) = 1/12 - 4^(n+2)/3 + 5^(n+2)/4. - R. J. Mathar, Mar 15 2011