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A169651 a(0)=a(1)=1, a(2)=2; thereafter a(n) = 3*a(n-1) + 3*2^(n-3) - 2. 2
1, 1, 2, 7, 25, 85, 277, 877, 2725, 8365, 25477, 77197, 233125, 702445, 2113477, 6352717, 19082725, 57297325, 171990277, 516167437, 1548895525, 4647473005, 13943991877, 41835121357, 125511655525, 376547549485, 1129667814277, 3389053774477, 10167261986725 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Arises in analyzing A169648.
Sequence in context: A145130 A048506 A335718 * A289446 A370022 A289598
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 07 2010
STATUS
approved

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Last modified July 12 20:37 EDT 2024. Contains 374252 sequences. (Running on oeis4.)