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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved