OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-21).
FORMULA
a(n) = (7^(n+1) - 3^(n+1))/4. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
a(n) = 10*a(n-1) - 21*a(n-2). - Philippe Deléham, Jan 01 2009
G.f.: x/(1-10*x+21*x^2). - Zerinvary Lajos, Apr 26 2009
E.g.f.: (d/dx)(exp(3*x)*(exp(4*x)-1)/4) = exp(3*x)*(7*exp(4*x) - 3)/4. - Wolfdieter Lang, Apr 13 2017
MATHEMATICA
Table[(7^(n+1) - 3^(n+1))/4, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
CoefficientList[Series[1/((1-3x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, -21}, {1, 10}, 30] (* Harvey P. Dale, Nov 07 2014 *)
PROG
(Sage) [lucas_number1(n, 10, 21) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009
(Magma) [(7^(n+1)-3^(n+1))/4: n in [0..30]]; // Vincenzo Librandi, Oct 09 2011
(PARI) Vec(1/((1-3*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved