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A046994 Number of Greek-key tours on a 3 X n board; i.e., self-avoiding walks on a 3 X n grid starting in the top left corner. 6
1, 3, 8, 17, 38, 78, 164, 332, 680, 1368, 2768, 5552, 11168, 22368, 44864, 89792, 179840, 359808, 720128, 1440512, 2882048, 5764608, 11531264, 23063552, 46131200, 92264448, 184537088, 369078272, 738172928, 1476354048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Posting by Thomas Womack (mert0236(AT)sable.ox.ac.uk) to sci.math newsgroup, Apr 21 1999.

LINKS

Robert Israel, Table of n, a(n) for n = 1..2985

FORMULA

a(1) = 1; a(2m) = Sum_{i = 2...2m-1} a(i) + 3*2^(m-1); a(2m+1) = Sum_{i = 2...2m} a(i) + 5*2^(m-1).

a(n) = 11*2^(n-3) - (4 + (-1)^n)*(2^((1/4)*(2n - 7 - (-1)^n))), n >= 2. - Nathaniel Johnston, Feb 03 2006

a(n) = 2*a(n-1)+2*a(n-2)-4*a(n-3) for n>4. G.f.: x*(1+x-x^3)/(1-2*x-2*x^2+4*x^3). - Colin Barker, Jul 19 2012

EXAMPLE

On a 3 X 3 board labeled 123 456 789 (reading across rows), 125478963 is such a tour.

MAPLE

A046994:=n->`if`(n=1, 1, 11*2^(n-3)-(4+(-1)^n)*(2^((1/4)*(2*n-7-(-1)^n)))): seq(A046994(n), n=1..30); # Wesley Ivan Hurt, Sep 14 2014

MATHEMATICA

CoefficientList[Series[(1 + x - x^3)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 14 2014 *)

CROSSREFS

Cf. A046995.

Sequence in context: A295061 A247374 A336512 * A058811 A101822 A354538

Adjacent sequences: A046991 A046992 A046993 * A046995 A046996 A046997

KEYWORD

nonn,walk

AUTHOR

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr)

EXTENSIONS

More terms and formula from Hugo van der Sanden

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)