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A094817 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) = 3. 1
2, 6, 19, 62, 206, 692, 2340, 7944, 27032, 92112, 314128, 1071776, 3657824, 12485696, 42623040, 145512576, 496787840, 1696093440, 5790732544, 19770612224, 67500721664, 230461137920, 786842059776, 2686443866112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)) 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)^2*(2*cos(r*Pi/8))^(2*n)).

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

G.f.: -x*(2-6*x+3*x^2) / ( (2*x-1)*(2*x^2-4*x+1) )

a(n) = A216232(n,n), for n>=1. - Philippe Deléham, Mar 21 2013

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

CROSSREFS

Sequence in context: A148464 A148465 A148466 * A033565 A094831 A033193

Adjacent sequences:  A094814 A094815 A094816 * A094818 A094819 A094820

KEYWORD

nonn,easy

AUTHOR

Herbert Kociemba, Jun 12 2004

STATUS

approved

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Last modified July 24 03:29 EDT 2021. Contains 346273 sequences. (Running on oeis4.)