OFFSET
0,2
LINKS
FORMULA
a(n) = (6^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).
a(n) = -6^n + 2*12^n.
E.g.f.: (d^2/dx^2)((((exp(6*x)-1)/6)^2)/2!) = -exp(6*x) + 2*exp(12*x).
a(n-1) = ((9+sqrt9)^n - (9-sqrt9)^n)/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
a(n) = 12*a(n-1) + 6^n, n >= 1. - Vincenzo Librandi, Feb 09 2011
a(n) = 18*a(n-1) - 72*a(n-2), n >= 2. - Vincenzo Librandi, Feb 09 2011
MATHEMATICA
Join[{a=1, b=18}, Table[c=18*b-72*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{18, -72}, {1, 18}, 20] (* Harvey P. Dale, Nov 25 2013 *)
PROG
(PARI) Vec(1/((1-6*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved