|
Search: id:A094052
|
|
|
| A094052 |
|
Number of walks of length n between two adjacent nodes in the cycle graph C_7. |
|
+0
1
|
|
| 0, 1, 0, 3, 0, 10, 1, 35, 9, 126, 55, 462, 286, 1717, 1365, 6451, 6188, 24463, 27132, 93518, 116281, 360031, 490337, 1394582, 2043275, 5430530, 8439210, 21242341, 34621041, 83411715, 141290436, 328589491, 574274008, 1297937234, 2326683921
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
In general a(n,m)=2^n/m*Sum_{k=0..m-1} Cos(2Pi*k/m)^(n+1) counts walks of length n between two adjacent nodes in the cycle graph C_m.
|
|
FORMULA
|
a(n)=2^n/7*Sum_{k=0..6} Cos(2Pi*k/7)^(n+1)
G.f.: x(1-x-x^2) / [(1-2x)(1+x-2x^2-x^3)].
|
|
MATHEMATICA
|
f[n_] := FullSimplify[ TrigToExp[ 2^n/7 Sum[ Cos[2Pi*k/7]^(n + 1), {k, 0, 6}]]]; Table[ f[n], {n, 0, 34}] (from Robert G. Wilson v Jun 01 2004)
|
|
CROSSREFS
|
Equals A095307(n+1) - A095308(n-1).
Sequence in context: A028850 A138364 A095364 this_sequence A161678 A081658 A119957
Adjacent sequences: A094049 A094050 A094051 this_sequence A094053 A094054 A094055
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 2004
|
|
|
Search completed in 0.002 seconds
|
