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A094821 Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 8 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 5. 1
1, 4, 15, 54, 190, 660, 2276, 7816, 26776, 91600, 313104, 1069728, 3653728, 12477504, 42606656, 145479808, 496722304, 1695962368, 5790470400, 19770087936, 67499673088, 230459040768, 786837865472, 2686435477504 (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)) counts (s(0), s(1), ..., s(2n)) such that 0 < s(i) < m and |s(i)-s(i-1)| = 1 for i = 1,2,....,2n, s(0) = j, s(2n) = k.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-10,4).

FORMULA

a(n)=(1/4)*Sum(r, 1, 7, Sin(3*r*Pi/8)Sin(5*r*Pi/8)(2Cos(r*Pi/8))^(2n)).

a(n)= 6a(n-1)-10a(n-2)+4a(n-3), n>=4

G.f.: -x*(x-1)^2 / ( (2*x-1)*(2*x^2-4*x+1) ).

4*a(n) = 2*A007052(n) -2^n. - R. J. Mathar, Nov 14 2019

CROSSREFS

Sequence in context: A090326 A291032 A006234 * A071723 A001559 A002311

Adjacent sequences:  A094818 A094819 A094820 * A094822 A094823 A094824

KEYWORD

nonn,easy

AUTHOR

Herbert Kociemba, Jun 12 2004

STATUS

approved

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Last modified October 29 18:53 EDT 2020. Contains 338067 sequences. (Running on oeis4.)