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A171160
a(n) = a(n-1) + 2*a(n-2) with a(0)=3, a(1)=4.
3
3, 4, 10, 18, 38, 74, 150, 298, 598, 1194, 2390, 4778, 9558, 19114, 38230, 76458, 152918, 305834, 611670, 1223338, 2446678, 4893354, 9786710, 19573418, 39146838, 78293674, 156587350, 313174698, 626349398, 1252698794, 2505397590, 5010795178, 10021590358
OFFSET
0,1
FORMULA
a(n) = (1/3)*(2*(-1)^n + 7*2^n), with n>=0. - Paolo P. Lava, Dec 14 2009
G.f.: -(x+3) / ((x+1)*(2*x-1)). - Colin Barker, Feb 10 2015
From Paul Curtz, Jun 03 2022: (Start)
a(n) = A078008(n) + A078008(n+1) + A078008(n+2).
a(n) = 2^(n+1) + A078008(n).
a(n) = A001045(n+3) - A001045(n).
(a(n) + a(n+1) = a(n+2) - a(n) = A005009(n).)
a(n) + a(n+3) = A175805(n).
a(n) = A062510(n) + A083582(n-1) with A083582(-1) = 3.
a(n) = A092297(n) + A154879(n). (End)
a(n) = 2*A062092(n-1), for n>0; 2*a(n) = A083595(n+1). - Paul Curtz, Jun 08 2022
MATHEMATICA
f[n_]:=2/(n+1); x=5; Table[x=f[x]; Numerator[x], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)
LinearRecurrence[{1, 2}, {3, 4}, 40] (* Harvey P. Dale, Sep 04 2013 *)
PROG
(PARI) Vec(-(x+3)/((x+1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Feb 10 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 04 2009
EXTENSIONS
Edited by N. J. A. Sloane, Dec 05 2009
More terms from J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010
More terms from Max Alekseyev, Apr 24 2010
STATUS
approved