cp's OEIS Frontend

A188154 Number of 9-step self-avoiding walks on an n X n square summed over all starting positions.

%I A188154 #10 Apr 27 2018 08:31:37
%S A188154 0,0,40,2640,14520,39792,78168,128688,191068,265280,351324,449200,
%T A188154 558908,680448,813820,959024,1116060,1284928,1465628,1658160,1862524,
%U A188154 2078720,2306748,2546608,2798300,3061824,3337180,3624368,3923388,4234240,4556924
%N A188154 Number of 9-step self-avoiding walks on an n X n square summed over all starting positions.
%C A188154 Row 9 of A188147.
%H A188154 R. H. Hardin, <a href="/A188154/b188154.txt">Table of n, a(n) for n = 1..50</a>
%F A188154 Empirical: a(n) = 5916*n^2 - 38192*n + 55600 for n>7.
%F A188154 Conjectures from _Colin Barker_, Apr 27 2018: (Start)
%F A188154 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 A188154 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.
%F A188154 (End)
%e A188154 Some solutions for 3 X 3:
%e A188154 ..3..4..5....1..2..3....3..4..5....9..2..1....3..4..5....9..4..3....7..6..5
%e A188154 ..2..7..6....8..7..4....2..9..6....8..3..4....2..1..6....8..5..2....8..3..4
%e A188154 ..1..8..9....9..6..5....1..8..7....7..6..5....9..8..7....7..6..1....9..2..1
%Y A188154 Cf. A188147.
%K A188154 nonn
%O A188154 1,3
%A A188154 _R. H. Hardin_, Mar 22 2011