cp's OEIS Frontend

A188147 T(n,k)=Number of n-step self-avoiding walks on a kXk square summed over all starting positions.

%I A188147 #8 Jul 22 2025 11:00:49
%S A188147 1,4,0,9,8,0,16,24,8,0,25,48,44,8,0,36,80,104,80,0,0,49,120,188,232,
%T A188147 104,0,0,64,168,296,456,432,128,0,0,81,224,428,752,972,800,112,0,0,
%U A188147 100,288,584,1120,1712,2112,1248,112,0,0,121,360,764,1560,2652,4008,4152,1976,40
%N A188147 T(n,k)=Number of n-step self-avoiding walks on a kXk square summed over all starting positions.
%C A188147 Table starts
%C A188147 .1.4...9...16....25....36.....49.....64.....81....100....121.....144.....169
%C A188147 .0.8..24...48....80...120....168....224....288....360....440.....528.....624
%C A188147 .0.8..44..104...188...296....428....584....764....968...1196....1448....1724
%C A188147 .0.8..80..232...456...752...1120...1560...2072...2656...3312....4040....4840
%C A188147 .0.0.104..432...972..1712...2652...3792...5132...6672...8412...10352...12492
%C A188147 .0.0.128..800..2112..4008...6472...9504..13104..17272..22008...27312...33184
%C A188147 .0.0.112.1248..4152..8752..14932..22672..31972..42832..55252...69232...84772
%C A188147 .0.0.112.1976..8160.19312..35024..55104..79528.108296.141408..178864..220664
%C A188147 .0.0..40.2640.14520.39792..78168.128688.191068.265280.351324..449200..558908
%C A188147 .0.0...0.3696.26000.82032.175312.303328.464304.657848.883928.1142544.1433696
%H A188147 R. H. Hardin, <a href="/A188147/b188147.txt">Table of n, a(n) for n = 1..264</a>
%F A188147 Empirical: T(1,k) = k^2
%F A188147 Empirical: T(2,k) = 4*k^2 - 4*k
%F A188147 Empirical: T(3,k) = 12*k^2 - 24*k + 8 for k>1
%F A188147 Empirical: T(4,k) = 36*k^2 - 100*k + 56 for k>2
%F A188147 Empirical: T(5,k) = 100*k^2 - 360*k + 272 for k>3
%F A188147 Empirical: T(6,k) = 284*k^2 - 1228*k + 1152 for k>4
%F A188147 Empirical: T(7,k) = 780*k^2 - 3960*k + 4432 for k>5
%F A188147 Empirical: T(8,k) = 2172*k^2 - 12500*k + 16096 for k>6
%F A188147 Empirical: T(9,k) = 5916*k^2 - 38192*k + 55600 for k>7
%F A188147 Empirical: T(10,k) = 16268*k^2 - 115548*k + 186528 for k>8
%e A188147 Some n=3 solutions for 3X3
%e A188147 ..1..0..0....0..0..0....0..0..3....0..0..0....0..0..0....0..0..0....0..0..0
%e A188147 ..2..0..0....0..3..0....0..0..2....0..3..2....0..1..0....0..0..3....0..0..0
%e A188147 ..3..0..0....1..2..0....0..0..1....0..0..1....3..2..0....0..1..2....1..2..3
%Y A188147 Row 2 is A033996(n-1)
%K A188147 nonn,tabl
%O A188147 1,2
%A A188147 _R. H. Hardin_ Mar 22 2011