0,2

P. H. Winston, Artificial Intelligence, (1977) 115-122, alpha-beta technique.

Harry J. Smith, Table of n, a(n) for n=0,...,500

a(2n) = 2*(3^n) - 1, a(2n+1) = 3^n + 3^(n+1) - 1.

Formula for b branches: a(2n)=2*(b^n)-1, a(2n+1)=b^n +b^(n+1) -1

G.f.= (1+2z-z^2)/[(1-z)(1-3*z^2)] - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2002

a(n)=(sqrt(3))^n(1+2/sqrt(3))+(1-2/sqrt(3))(-sqrt(3))^n-1. - Paul Barry (pbarry(AT)wit.ie), Apr 17 2004

a(2n+1) = 2*a(2n) + 1, a(15) = a(2*7+1) = 2*a(14) + 1 = 2*4373 + 1 = 8747.

A060647 := proc(n, b) option remember: if n mod 2 = 0 then RETURN(2*b^(n/2)-1) else RETURN(b^((n-1)/2) +b^((n+1)/2)-1) fi: end: for n from 0 to 60 do printf(`%d, `, A060647(n, 3)) od:

a[0]:=1:a[1]:=3:for n from 2 to 100 do a[n]:=3*a[n-2]+2 od: seq(a[n], n=0..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008

f[n_] := Simplify[Sqrt[3]^n(1 + 2/Sqrt[3]) + (1 - 2/Sqrt[3])(-Sqrt[3])^n - 1]; Table[ f[n], {n, 0, 34}] (* or *)

f[n_] := If[ EvenQ[n], 2(3^(n/2)) - 1, 3^((n - 1)/2) + 3^((n + 1)/2) - 1]; Table[ f[n], {n, 0, 34}] (* or *)

CoefficientList[ Series[(1 + 2x - x^2)/((1 - x)(1 - 3x^2)), {x, 0, 35}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 17 2005)

(PARI) { for (n=0, 500, if (n%2==0, a=2*(3^(n/2)) - 1, m=(n - 1)/2; a=3^m + 3^(m + 1) - 1); write("b060647.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 09 2009]

For b=2 see A052955.

Equals A068911(n+1)-1.

Sequence in context: A006170 A147071 A006171 this_sequence A155989 A125557 A007455

Adjacent sequences: A060644 A060645 A060646 this_sequence A060648 A060649 A060650

easy,nonn

Frank Ellermann (Frank.Ellermann(AT)t-online.de), Apr 17 2001

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 19 2001