A187168 Number of 7-step self-avoiding walks on an n X n X n cube summed over all starting positions.

0, 192, 25344, 177120, 568248, 1298016, 2466510, 4175136, 6525450, 9619008, 13557366, 18442080, 24374706, 31456800, 39789918, 49475616, 60615450, 73310976, 87663750, 103775328, 121747266, 141681120, 163678446, 187840800, 214269738

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn
• walk

Comments

Row 7 of A187162.

Examples

			A solution for 3 X 3 X 3:
..0..0..0.....0..0..0.....0..0..0
..0..0..0.....1..2..0.....0..0..0
..7..0..0.....6..3..0.....5..4..0
		

Links

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

Crossrefs

Cf. A187162.

Formula

Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.

Conjectures from Colin Barker, Apr 21 2018: (Start)

G.f.: 6*x^2*(32 + 4096*x + 12816*x^2 + 1844*x^3 - 2240*x^4 + 133*x^5 + 220*x^6 + 25*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.

(End)