The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094659 Number of closed walks of length n at a vertex of the cyclic graph on 7 nodes C_7. 2
 1, 0, 2, 0, 6, 0, 20, 2, 70, 18, 252, 110, 924, 572, 3434, 2730, 12902, 12376, 48926, 54264, 187036, 232562, 720062, 980674, 2789164, 4086550, 10861060, 16878420, 42484682, 69242082, 166823430, 282580872, 657178982, 1148548016, 2595874468 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In general a(n,m)=2^n/m*Sum_{k=0..m-1} cos(2Pi*k/m)^n) counts closed walks of length n at a vertex of the cyclic graph on m nodes C_m. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1, 4, -3, -2). FORMULA a(n ) =2^n/7*Sum_{k=0..6} cos(2Pi*k/7)^n). a(n) = 7(a(n-2) - 2a(n-4) + a(n-6)) + 2a(n-7). G.f.: (1-x-2x^2+x^3)/((2x-1)(-1-x+2x^2+x^3)). a(0)=1, a(1)=0, a(2)=2, a(3)=0, a(n)=a(n-1)+4*a(n-2)-3*a(n-3)-2*a(n-4). - Harvey P. Dale, Jun 12 2014 7*a(n) = 2^n +2*A094648(n). - R. J. Mathar, Nov 03 2020 MATHEMATICA f[n_] := FullSimplify[ TrigToExp[ 2^n/7 Sum[Cos[2Pi*k/7]^n, {k, 0, 6}]]]; Table[ f[n], {n, 0, 36}] (* Robert G. Wilson v, Jun 09 2004 *) LinearRecurrence[{1, 4, -3, -2}, {1, 0, 2, 0}, 40] (* Harvey P. Dale, Jun 12 2014 *) CROSSREFS Sequence in context: A081153 A126869 A094233 * A321907 A137437 A183189 Adjacent sequences:  A094656 A094657 A094658 * A094660 A094661 A094662 KEYWORD nonn,easy AUTHOR Herbert Kociemba, Jun 06 2004 EXTENSIONS More terms from Robert G. Wilson v, Jun 09 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 04:10 EST 2021. Contains 349417 sequences. (Running on oeis4.)