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A094297 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 2, s(n) = 2. 1
1, 3, 7, 18, 46, 120, 316, 840, 2248, 6048, 16336, 44256, 120160, 326784, 889792, 2424960, 6613120, 18043392, 49247488, 134450688, 367134208, 1002645504, 2738510848, 7480215552, 20433258496, 55818559488, 152486858752 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general a(n,m,j,k)=2/m*Sum(r,1,m-1,Sin(j*r*Pi/m)Sin(k*r*Pi/m)(1+2Cos(Pi*r/m))^n) is the number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < m and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = j, s(n) = k.

LINKS

Table of n, a(n) for n=1..27.

Robert Munafo, Sequences Related to Floretions

FORMULA

a(n)=(1/3)*Sum(k, 1, 5, Sin(Pi*k/3)^2(1+2Cos(Pi*k/6))^n) or a(n)=( 2^n+(1-Sqrt(3))^n + (1+Sqrt(3))^n )/4

(a(n)) seems to be given by tesseq(- 2'i + 2'j + 2'k - 2i' + 2j' + 2k' - 2'ii' + 2'jj' - 'kk' - 2.5'ik' - 1.5'jk' - 2.5'ki' - 1.5'kj' - e) (disregarding signs) - Creighton Dement, Nov 17 2004

CROSSREFS

First differences of A038508.

Sequence in context: A116413 A052960 A059512 * A026107 A173765 A027969

Adjacent sequences:  A094294 A094295 A094296 * A094298 A094299 A094300

KEYWORD

easy,nonn

AUTHOR

Herbert Kociemba, Jun 02 2004

STATUS

approved

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Last modified June 22 07:47 EDT 2017. Contains 288605 sequences.