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A187166 Number of 5-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2
0, 144, 3240, 14256, 37470, 77184, 137754, 223536, 338886, 488160, 675714, 905904, 1183086, 1511616, 1895850, 2340144, 2848854, 3426336, 4076946, 4805040, 5614974, 6511104, 7497786, 8579376, 9760230, 11044704, 12437154, 13941936, 15563406 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 5 of A187162.

LINKS

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

FORMULA

Empirical: a(n) = 726*n^3 - 2640*n^2 + 2688*n - 720 for n>3.

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

G.f.: 6*x^2*(24 + 444*x + 360*x^2 - 115*x^3 + 4*x^4 + 9*x^5) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.

(End)

EXAMPLE

A solution for 2 X 2 X 2:

..5..0.....4..1

..0..0.....3..2

CROSSREFS

Cf. A187162.

Sequence in context: A223300 A330837 A252182 * A231836 A268968 A253134

Adjacent sequences:  A187163 A187164 A187165 * A187167 A187168 A187169

KEYWORD

nonn,walk

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)