OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (16,-76,96).
FORMULA
G.f.: 1/((1-2*x)*(1-6*x)*(1-8*x)).
a(n) = 2^(n-1)*(2^(2*n+5) - 3^(n+3) + 1)/3. - Zerinvary Lajos, Jun 05 2009
From Vincenzo Librandi, Sep 01 2011: (Start)
a(n) = 16*a(n-1) - 76*a(n-2) + 96*a(n-3) for n > 2;
a(n) = 14*a(n-1) - 48*a(n-2) + 2^n for n > 1. (End)
MATHEMATICA
CoefficientList[Series[1/((1-2x)(1-6x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -76, 96}, {1, 16, 180}, 30] (* Harvey P. Dale, Feb 21 2015 *)
PROG
(Sage) [((8^n - 2^n)/6-(6^n - 2^n)/4)/2 for n in range(2, 21)] # Zerinvary Lajos, Jun 05 2009
(Magma) [2^(n-1)*(2^(2*n+5)-3^(n+3)+1)/3: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved