The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors 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. 3
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)*(2*cos(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
László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
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) / ( (x-1)*(x^3-9*x^2+6*x-1) ).
3*a(n) = A094829(n+2) -2*A094829(n+1) -2*A094829(n)-1. - R. J. Mathar, Nov 14 2019
MATHEMATICA
LinearRecurrence[{7, -15, 10, -1}, {1, 4, 14, 48}, 30] (* Harvey P. Dale, Jul 09 2020 *)
CROSSREFS
Sequence in context: A007070 A204089 A092489 * A094667 A370051 A099376
KEYWORD
nonn,easy
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)