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Search: id:A094833
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| A094833 |
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Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 5. |
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+0
2
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| 1, 4, 15, 55, 199, 714, 2548, 9061, 32148, 113887, 403051, 1425471, 5039254, 17809336, 62928201, 222324436, 785402143, 2774421135, 9800231959, 34617003682, 122274355596, 431893332397, 1525507797700, 5388281150223
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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a(n+1)=3*a(n)+A094832(n-1) . - Philippe DELEHAM, Mar 20 2007
a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/3)Sin(5*r*Pi/9)(2Cos(r*Pi/9))^(2n)) a(n)=6a(n-1)-9a(n-2)+a(n-3) G.f.: (-x+2x^2)/(-1+6x-9x^2+x^3)
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CROSSREFS
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Sequence in context: A002311 A102349 A126932 this_sequence A039717 A026013 A050183
Adjacent sequences: A094830 A094831 A094832 this_sequence A094834 A094835 A094836
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KEYWORD
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nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jun 13 2004
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