Search: id:A094287
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%I A094287
%S A094287 1,2,4,9,21,51,127,323,835,2188,5798,15510,41822,113531,309937,850118,
%T A094287 2340918,6466953,17913087,49726649,138287113,385126811,1073832695,
%U A094287 2996974774,8370739326,23394528640,65415732100,182989086965
%N A094287 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 7 and |s(i) - 
               s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 1.
%C A094287 In general a(n)=2/m*Sum_{k=1..m} 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=7.
%F A094287 a(n)=(2/7)*Sum_{k=1..6} Sin(Pi*k/7)^2(1+2Cos(Pi*k/7))^n
%t A094287 f[n_] := FullSimplify[ TrigToExp[(2/7)*Sum[ Sin[Pi*k/7]^2(1 + 2Cos[Pi*k/
               7])^n, {k, 1, 6}]]]; Table[ f[n], {n, 28}] (from Robert G. Wilson 
               v Jun 18 2004)
%Y A094287 Sequence in context: A051529 A005207 A094286 this_sequence A094288 A166587 
               A086246
%Y A094287 Adjacent sequences: A094284 A094285 A094286 this_sequence A094288 A094289 
               A094290
%K A094287 easy,nonn
%O A094287 1,2
%A A094287 Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004

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