A016200 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-6*x)).

1, 9, 61, 381, 2317, 13965, 83917, 503757, 3023053, 18139341, 108838093, 653032653, 3918204109, 23509241037, 141055478989, 846332939469, 5077997767885, 30467986869453, 182807921741005, 1096847531494605, 6581085191064781, 39486511150582989, 236919066911886541, 1421514401488096461

Offset

0,2

Links

Muniru A Asiru, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Formula

a(n) = (9*6^n - 5*2^n + 1)/5. - Bruno Berselli, Feb 09 2011

a(0)=1, a(n) = 6*a(n-1) + 2^(n+1) - 1. - Vincenzo Librandi, Feb 09 2011

a(n) = Sum_{k=0..n} 2^(n-1-k)*(3^(n+1-k) - 1). - J. M. Bergot, Feb 06 2018

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(x)*(9*exp(5*x) - 5*exp(x) + 1)/5.

a(n) = A016129(n+1) - A003464(n+2) = A241275(n+2)/5.

a(n) = 9*a(n-1) - 20*a(n-2) + 12*a(n-3). (End)

Maple

seq((9*6^n-5*2^n+1)/5, n=0..100); # Muniru A Asiru, Feb 06 2018

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{9, -20, 12}, {1, 9, 61}, 30] (* Harvey P. Dale, Aug 23 2025 *)

Prog

(GAP) List([0..100], n->(9*6^n-5*2^n+1)/5); # Muniru A Asiru, Feb 06 2018

Crossrefs

Cf. A003464, A016129, A241275.

Sequence in context: A005060 A125346 A190666 * A001454 A243877 A200674

Adjacent sequences: A016197 A016198 A016199 * A016201 A016202 A016203

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved