Search: id:A094821
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%I A094821
%S A094821 1,4,15,54,190,660,2276,7816,26776,91600,313104,1069728,3653728,
%T A094821 12477504,42606656,145479808,496722304,1695962368,5790470400,
%U A094821 19770087936,67499673088,230459040768,786837865472,2686435477504
%N A094821 Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 8 and |s(i) - 
               s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 5.
%C A094821 In general a(n)= 2/m*Sum(r,1,m-1,Sin(r*j*Pi/m)Sin(r*k*Pi/m)(2Cos(r*Pi/
               m))^(2n)) counts (s(0), s(1), ..., s(2n)) such that 0 < s(i) < m 
               and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n, s(0) = j, s(2n) = k.
%F A094821 a(n)=(1/4)*Sum(r, 1, 7, Sin(3*r*Pi/8)Sin(5*r*Pi/8)(2Cos(r*Pi/8))^(2n)) 
               a(n)= 6a(n-1)-10a(n-2)+4a(n-3), n>=4 G.f.: (1-2x+2x^2)/(4(-1+2x)(-1+4x-2x^2))
%Y A094821 Sequence in context: A164619 A090326 A006234 this_sequence A071723 A001559 
               A002311
%Y A094821 Adjacent sequences: A094818 A094819 A094820 this_sequence A094822 A094823 
               A094824
%K A094821 nonn
%O A094821 1,2
%A A094821 Herbert Kociemba (kociemba(AT)t-online.de), Jun 12 2004

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