OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-11,6). - R. J. Mathar, Apr 20 2010
FORMULA
G.f.: (1 - 5*x + 7*x^2 - x^4)/((1-x)*(1-2*x)*(1-3*x)). [corrected by Georg Fischer, May 11 2019]
a(n) = 4*3^(n-2) - 3*2^(n-2) + 1, n>1. - R. J. Mathar, Apr 20 2010
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); a(0)=1, a(1)=1, a(2)=2, a(3)=7, a(4)=25. - Harvey P. Dale, Nov 23 2011
E.g.f.: (11 + 36*exp(x) - 27*exp(2*x) + 16*exp(3*x) + 6*x)/36. - Stefano Spezia, Dec 24 2021
MAPLE
a:=n->if n <= 1 then 1 elif n=2 then 2 else 3*a(n-1)+3*2^(n-3)-2; fi;
MATHEMATICA
Join[{1, 1}, RecurrenceTable[{a[2]==2, a[n]==3a[n-1]+3 2^(n-3)-2}, a, {n, 30}]] (* or *) Join[{1, 1}, LinearRecurrence[{6, -11, 6}, {2, 7, 25}, 30]](* Harvey P. Dale, Nov 23 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 07 2010
STATUS
approved