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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

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