|
Search: id:A094306
|
|
|
| A094306 |
|
Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 2, s(n) = 4. |
|
+0
2
|
|
| 1, 3, 10, 30, 88, 252, 712, 1992, 5536, 15312, 42208, 116064, 318592, 873408, 2392192, 6547584, 17912320, 48985344, 133926400, 366085632, 1000548352, 2734316544, 7471826944, 20416481280, 55785005056, 152419749888
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
COMMENT
|
In general a(n,m,j,k)=2/m*Sum_{r=1..m-1} Sin(j*r*Pi/m)Sin(k*r*Pi/m)(1+2Cos(Pi*r/m))^n) is the number of (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) = j, s(n) = k.
|
|
FORMULA
|
a(n)=( (1-Sqrt(3))^n + (1+Sqrt(3))^n -2^n )/4; a(n)=(1/3)*Sum_{k=1..5} Sin(Pi*k/3)Sin(2Pi*k/3)(1+2Cos(Pi*k/6))^n
|
|
MATHEMATICA
|
f[n_] := FullSimplify[ TrigToExp[(1/3)Sum[ Sin[Pi*k/3] Sin[2Pi*k/3] (1 + 2Cos[Pi*k/6])^n, {k, 1, 5}]]]; Table[ f[n], {n, 2, 27}] (from Robert G. Wilson v Jun 18 2004)
|
|
CROSSREFS
|
Sequence in context: A092756 A027205 A026937 this_sequence A026109 A026327 A014531
Adjacent sequences: A094303 A094304 A094305 this_sequence A094307 A094308 A094309
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
|
|
|
Search completed in 0.002 seconds
|
