login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..24.

FORMULA

a(n) = (2/9)*sum(r=1..8, sin(r*Pi/9)*sin(4*r*Pi/9)*(2*cos(r*Pi/9))^(2*n+1)).

a(n) = 7*a(n-1) - 15*a(n-2) + 10*a(n-3) - a(n-4).

G.f.: x*(-1+3*x-x^2)/(-1+7*x-15*x^2+10*x^3-x^4).

CROSSREFS

Sequence in context: A007070 A204089 A092489 * A094667 A099376 A002057

Adjacent sequences:  A094824 A094825 A094826 * A094828 A094829 A094830

KEYWORD

nonn

AUTHOR

Herbert Kociemba, Jun 13 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 14:46 EST 2018. Contains 299334 sequences. (Running on oeis4.)