0,3

First differences are given by A026150.

The number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 2, s(n) = 3. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004

Tanya Khovanova, Recursive Sequences

a(n)=((1 + sqrt(3))^n - (1 - sqrt(3))^n)/(2*sqrt(3)) a(n)=Sum{k=0..n, binomial(n, 2k+1)3^k} G.f.: x/(1-2x-2x^2)

Binomial transform of expansion of sinh(sqrt(3)x)/sqrt(3) (0, 1, 0, 3, 0, 9, ...). E.g.f.: exp(x)sinh(sqrt(3)x)/sqrt(3). - Paul Barry (pbarry(AT)wit.ie), May 09 2003

a(n)=(1/3)*Sum(k, 1, 5, Sin(Pi*k/2)Sin(2Pi*k/3)(1+2Cos(Pi*k/6))^n) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004

with(combstruct):ZL0:=S=Prod(Sequence(Prod(a, Sequence(b))), b):ZL1:=Prod(begin_blockP, Z, end_blockP):ZL2:=Prod(begin_blockLR, Z, Sequence(Prod(mu_length, Z), card>=1), end_blockLR): ZL3:=Prod(begin_blockRL, Sequence(Prod(mu_length, Z), card>=1), Z, end_blockRL):Q:=subs([a=Union(ZL2, ZL2, ZL2), b=ZL1], ZL0), begin_blockP=Epsilon, end_blockP=Epsilon, begin_blockLR=Epsilon, end_blockLR=Epsilon, begin_blockRL=Epsilon, end_blockRL=Epsilon, mu_length=Epsilon:temp15:=draw([S, {Q}, unlabelled], size=15):seq(count([S, {Q}, unlabelled], size=n)/3, n=2..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2008

Expand[Table[((1 + Sqrt[3])^n - (1 - Sqrt[3])^n)/(2Sqrt[3]), {n, 0, 30}]] - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006

Cf. A002605, A028859.

Essentially the same as A002605. Equals (1/3) A083337. First differences of A077846. Pairwise sums of A028860 and |A077917|.

Sequence in context: A118041 A105073 A002605 this_sequence A026134 A105696 A074413

Adjacent sequences: A080950 A080951 A080952 this_sequence A080954 A080955 A080956

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Feb 26 2003

Definition corrected by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 18 2006