A016150 Expansion of 1/((1-4x)(1-7x)).

1, 11, 93, 715, 5261, 37851, 269053, 1899755, 13363821, 93808891, 657710813, 4608169995, 32273967181, 225984879131, 1582162589373, 11076211867435, 77537778039341, 542781626144571, 3799540102488733

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-28).

Formula

a(n) = (7^(n+1) - 4^(n+1))/3. - Barry E. Williams, Jan 13 2000

a(n) = 11*a(n-1) - 28*a(n-2) for n>0, a(0)=1. - Barry E. Williams, Jan 13 2000

a(n) = Sum_{k=0..n} 7^k*4^(n-k). - Bruno Berselli, Aug 07 2013

Mathematica

Join[{a=1, b=11}, Table[c=11*b-28*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011 *)
CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 24 2013 *)
LinearRecurrence[{11, -28}, {1, 11}, 20] (* Harvey P. Dale, Mar 11 2020 *)

Prog

(Sage) [lucas_number1(n, 11, 28) for n in range(1, 20)] /* Zerinvary Lajos, Apr 27 2009 */
(PARI) Vec(1/((1-4*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

Sequence in context: A044643 A025507 A081575 * A115203 A164547 A298925

Adjacent sequences: A016147 A016148 A016149 * A016151 A016152 A016153

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved