|
Search: id:A094827
|
|
|
| A094827 |
|
Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 9 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = 1, s(2n+1) = 4. |
|
+0
1
|
|
| 1, 4, 14, 48, 165, 571, 1988, 6953, 24396, 85786, 302104, 1064945, 3756519, 13256712, 46796545, 165225380, 583440086, 2060408640, 7276716445, 25700060995, 90770326604, 320598127113, 1132355884236, 3999522488002
(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+1)) counts (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = j, s(2n+1) = k.
|
|
FORMULA
|
a(n)=(2/9)*Sum(r, 1, 8, Sin(r*Pi/9)Sin(4*r*Pi/9)(2Cos(r*Pi/9))^(2n+1)) a(n)=7a(n-1)-15a(n-2)+10a(n-3)-a(n-4) G.f.: x(-1+3x-x^2)/(-1+7x-15x^2+10x^3-x^4)
|
|
CROSSREFS
|
Sequence in context: A127359 A007070 A092489 this_sequence A094667 A002057 A099376
Adjacent sequences: A094824 A094825 A094826 this_sequence A094828 A094829 A094830
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Herbert Kociemba (kociemba(AT)t-online.de), Jun 13 2004
|
|
|
Search completed in 0.002 seconds
|
