|
Search: id:A094821
|
|
|
| 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. |
|
+0
1
|
|
| 1, 4, 15, 54, 190, 660, 2276, 7816, 26776, 91600, 313104, 1069728, 3653728, 12477504, 42606656, 145479808, 496722304, 1695962368, 5790470400, 19770087936, 67499673088, 230459040768, 786837865472, 2686435477504
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
FORMULA
|
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))
|
|
CROSSREFS
|
Sequence in context: A164619 A090326 A006234 this_sequence A071723 A001559 A002311
Adjacent sequences: A094818 A094819 A094820 this_sequence A094822 A094823 A094824
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Herbert Kociemba (kociemba(AT)t-online.de), Jun 12 2004
|
|
|
Search completed in 0.002 seconds
|
