A223332 Rolling cube footprints: number of 3 X n 0..7 arrays starting with 0 where 0..7 label vertices of a cube and every array movement to a horizontal or antidiagonal neighbor moves along a corresponding cube edge.

64, 243, 3969, 64827, 1059723, 17324685, 283231809, 4630406067, 75700050363, 1237579942725, 20232537609249, 330771018512907, 5407599817782603, 88405979220238365, 1445302430884160289, 23628482316968449347

Offset: 1

Author

R. H. Hardin, Mar 19 2013

Keywords

• nonn

Comments

Row 3 of A223331.

Examples

			Some solutions for n=3:
  0 2 6    0 4 6    0 2 6    0 1 5    0 2 3    0 1 5    0 2 6
  6 7 6    6 2 3    3 7 5    5 4 6    3 7 6    5 7 3    0 4 0
  3 7 6    6 2 0    6 4 6    6 2 0    6 7 3    6 7 6    6 4 6
Vertex neighbors:
  0 -> 1 2 4
  1 -> 0 3 5
  2 -> 0 3 6
  3 -> 1 2 7
  4 -> 0 5 6
  5 -> 1 4 7
  6 -> 2 4 7
  7 -> 3 5 6
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A223331.

Formula

Empirical: a(n) = 18*a(n-1) - 27*a(n-2) for n>4.

Conjectures from Colin Barker, Aug 19 2018: (Start)

G.f.: x*(64 - 909*x + 1323*x^2 - 54*x^3) / (1 - 18*x + 27*x^2).

a(n) = (49/54)*((9-3*sqrt(6))^n + (3*(3+sqrt(6)))^n) for n>2.

(End)