A016304 Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)).

1, 15, 157, 1419, 11869, 94731, 733069, 5551323, 41378557, 304766187, 2224062061, 16112628987, 116053574365, 831966057483, 5941308640333, 42294437942811, 300292730428093, 2127439102098219, 15044413649559085

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (15,-68,84)

Formula

a(n) = (7^(n+2) - 2^(n+2))/5-(6^(n+2) - 2^(n+2))/4. - Zerinvary Lajos, Jun 05 2009 [corrected by Joerg Arndt, Aug 25 2011]

From Vincenzo Librandi_, Aug 25 2011: (Start)

a(0)=1, a(1)=15, a(2)=157, a(n) = 15*a(n-1) - 68*a(n-2) + 84*a(n-3);

a(0)=1, a(1)=15, a(n) = 13*a(n-1) - 42*a(n-2) + 2^n. (End)

Mathematica

CoefficientList[Series[1/((1-2x)(1-6x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -68, 84}, {1, 15, 157}, 30]

Prog

(Sage) [(7^n - 2^n)/5-(6^n - 2^n)/4 for n in range(2, 21)] # Zerinvary Lajos, Jun 05 2009
(Magma) [ n eq 1 select 1 else n eq 2 select 15 else n eq 3 select 157 else 15*Self(n-1)-68*Self(n-2) +84*Self(n-3): n in [1..20] ]; // Vincenzo Librandi, Aug 25 2011
(PARI) Vec(1/((1-2*x)*(1-6*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

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

Sequence in context: A341918 A099915 A110557 * A016849 A300077 A367497

Adjacent sequences: A016301 A016302 A016303 * A016305 A016306 A016307

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved