A188154 - OEIS

%I #10 Apr 27 2018 08:31:37

%S 0,0,40,2640,14520,39792,78168,128688,191068,265280,351324,449200,

%T 558908,680448,813820,959024,1116060,1284928,1465628,1658160,1862524,

%U 2078720,2306748,2546608,2798300,3061824,3337180,3624368,3923388,4234240,4556924

%N Number of 9-step self-avoiding walks on an n X n square summed over all starting positions.

%C Row 9 of A188147.

%H R. H. Hardin, <a href="/A188154/b188154.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 5916*n^2 - 38192*n + 55600 for n>7.

%F Conjectures from _Colin Barker_, Apr 27 2018: (Start)

%F G.f.: 4*x^3*(10 + 630*x + 1680*x^2 + 1028*x^3 - 72*x^4 - 240*x^5 - 71*x^6 - 7*x^7) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

%F (End)

%e Some solutions for 3 X 3:

%e ..3..4..5....1..2..3....3..4..5....9..2..1....3..4..5....9..4..3....7..6..5

%e ..2..7..6....8..7..4....2..9..6....8..3..4....2..1..6....8..5..2....8..3..4

%e ..1..8..9....9..6..5....1..8..7....7..6..5....9..8..7....7..6..1....9..2..1

%Y Cf. A188147.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 22 2011