A016295 Expansion of 1/((1-2x)(1-5x)(1-6x)).

1, 13, 117, 905, 6461, 43953, 289717, 1868425, 11861421, 74423393, 462815717, 2858273145, 17556537181, 107373722833, 654414852117, 3977351721065, 24118423433741, 145982106270273, 882250466222917

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (13,-52,60).

Crossrefs

Cf. A016127, A016129, A016130, A016311, A016316, A016321, A016325. - Zerinvary Lajos, Jun 05 2009

Programs

Mathematica

LinearRecurrence[{13,-52,60},{1,13,117},20] (* Harvey P. Dale, Mar 26 2016 *)

Sage

[(6^n - 2^n)/4-(5^n - 2^n)/3 for n in range(2,21)] # Zerinvary Lajos, Jun 05 2009

Formula

a(n) = A016129(n+1) - A016127(n+1). - Zerinvary Lajos, Jun 05 2009

a(n) = 13*a(n-1) - 52*a(n-2) + 60*a(n-3), n >= 3.

a(n) = 11*a(n-1) - 30*a(n-2) + 2^n, n >= 2. - Vincenzo Librandi, Mar 16 2011

a(n) = 7*a(n-1) - 10*a(n-2) + 6^n, n >= 2. - Vincenzo Librandi, Mar 16 2011

a(n) = 8*a(n-1) - 12*a(n-2) + 5^n, n >= 2. - Vincenzo Librandi, Mar 16 2011

a(n) = -5^(n+2)/3 + 9*6^n + 2^n/3. - R. J. Mathar, Mar 18 2011