%I A094288
%S A094288 1,2,4,9,21,51,127,323,835,2188,5798,15511,41835,113633,310557,853333,
%T A094288 2355861,6531062,18171848,50722229,141973073,398351055,1120056347,
%U A094288 3155043447,8901325751,25147423616,71127785002,201381834019
%N A094288 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 8 and |s(i) - 
               s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1.
%C A094288 In general a(n)=2/m*Sum_{k=1..m-1} Sin(Pi*k/m)^2(1+2Cos(Pi*k/m))^n counts 
               the (s(0), s(1), ..., s(n)) such that 0 < s(i) < m and |s(i) - s(i-1)| 
               <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1. Here is m=8.
%F A094288 a(n)=(1/4)*Sum_{k=1..7} Sin(Pi*k/8)^2(1+2Cos(Pi*k/8))^n
%t A094288 f[n_] := FullSimplify[ TrigToExp[(1/4)*Sum[Sin[Pi*k/8]^2(1 + 2Cos[Pi*k/
               8])^n, {k, 1, 7}]]]; Table[ f[n], {n, 28}] (from Robert G. Wilson 
               v Jun 18 2004)
%Y A094288 This is a different sequence from the Motzkin numbers, A001006.
%Y A094288 Sequence in context: A005207 A094286 A094287 this_sequence A166587 A086246 
               A001006
%Y A094288 Adjacent sequences: A094285 A094286 A094287 this_sequence A094289 A094290 
               A094291
%K A094288 easy,nonn
%O A094288 1,2
%A A094288 Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004