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A187167 Number of 6-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2
0, 240, 9504, 51504, 148224, 320328, 588924, 975216, 1500408, 2185704, 3052308, 4121424, 5414256, 6952008, 8755884, 10847088, 13246824, 15976296, 19056708, 22509264, 26355168, 30615624, 35311836, 40465008, 46096344, 52227048, 58878324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..50

FORMULA

Empirical: a(n) = 3534*n^3 - 15366*n^2 + 19536*n - 7056 for n>4.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 12*x^2*(20 + 712*x + 1244*x^2 - 144*x^3 - 110*x^4 + 37*x^5 + 8*x^6) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.

(End)

EXAMPLE

A solution for 2 X 2 X 2:

..0..6.....0..1

..4..5.....3..2

CROSSREFS

Row 6 of A187162.

Sequence in context: A008340 A252183 A251434 * A282227 A268902 A232994

Adjacent sequences:  A187164 A187165 A187166 * A187168 A187169 A187170

KEYWORD

nonn,walk

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)