A016149 Expansion of g.f. 1/((1 - 4*x)*(1 - 6*x)).

1, 10, 76, 520, 3376, 21280, 131776, 807040, 4907776, 29708800, 179301376, 1080002560, 6496792576, 39047864320, 234555621376, 1408407470080, 8454739787776, 50745618595840, 304542431051776, 1827529464217600, 10966276296933376, 65802055828111360, 394829927154712576

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (10,-24).

Formula

From Barry E. Williams, Jan 13 2000: (Start)

a(n) = 10*a(n-1) - 24*a(n-2) for n>1, a(0)=1.

a(n) = ((6^(n+1)) - 4^(n+1))/2. (End)

a(n) = A081199(n+1). Binomial transform of A080961. - R. J. Mathar, Sep 18 2008

a(n) = Sum_{k=0..n} 6^k*4^(n-k). - Bruno Berselli, Aug 07 2013

E.g.f.: exp(4*x)*(3*exp(2*x) - 2). - Stefano Spezia, Jul 23 2024

Maple

seq(add(2^(2*n-k)*binomial(n, k)/2, k=1..n), n=1..19); # Zerinvary Lajos, Apr 18 2009

Mathematica

Join[{a=1, b=10}, Table[c=10*b-24*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
LinearRecurrence[{10, -24}, {1, 10}, 30]  (* or *) CoefficientList[ Series[ 1/(1-10 x+24 x^2), {x, 0, 30}], x] (* Harvey P. Dale, Apr 24 2011 *)

Prog

(SageMath) [lucas_number1(n, 10, 24) for n in range(1, 20)] # Zerinvary Lajos, Apr 26 2009
(PARI) Vec(1/((1-4*x)*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

Cf. A081199, A080961.

Sequence in context: A108277 A061319 A223994 * A081199 A351132 A198692

Adjacent sequences: A016146 A016147 A016148 * A016150 A016151 A016152

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved