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

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, 104, 0, 0, 64, 168, 296, 456, 432, 128, 0, 0, 81, 224, 428, 752, 972, 800, 112, 0, 0, 100, 288, 584, 1120, 1712, 2112, 1248, 112, 0, 0, 121, 360, 764, 1560, 2652, 4008, 4152, 1976, 40

Offset

1,2

Comments

Table starts

.1.4...9...16....25....36.....49.....64.....81....100....121.....144.....169

.0.8..24...48....80...120....168....224....288....360....440.....528.....624

.0.8..44..104...188...296....428....584....764....968...1196....1448....1724

.0.8..80..232...456...752...1120...1560...2072...2656...3312....4040....4840

.0.0.104..432...972..1712...2652...3792...5132...6672...8412...10352...12492

.0.0.128..800..2112..4008...6472...9504..13104..17272..22008...27312...33184

.0.0.112.1248..4152..8752..14932..22672..31972..42832..55252...69232...84772

.0.0.112.1976..8160.19312..35024..55104..79528.108296.141408..178864..220664

.0.0..40.2640.14520.39792..78168.128688.191068.265280.351324..449200..558908

.0.0...0.3696.26000.82032.175312.303328.464304.657848.883928.1142544.1433696

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical: T(1,k) = k^2

Empirical: T(2,k) = 4*k^2 - 4*k

Empirical: T(3,k) = 12*k^2 - 24*k + 8 for k>1

Empirical: T(4,k) = 36*k^2 - 100*k + 56 for k>2

Empirical: T(5,k) = 100*k^2 - 360*k + 272 for k>3

Empirical: T(6,k) = 284*k^2 - 1228*k + 1152 for k>4

Empirical: T(7,k) = 780*k^2 - 3960*k + 4432 for k>5

Empirical: T(8,k) = 2172*k^2 - 12500*k + 16096 for k>6

Empirical: T(9,k) = 5916*k^2 - 38192*k + 55600 for k>7

Empirical: T(10,k) = 16268*k^2 - 115548*k + 186528 for k>8

Example

Some n=3 solutions for 3X3
..1..0..0....0..0..0....0..0..3....0..0..0....0..0..0....0..0..0....0..0..0
..2..0..0....0..3..0....0..0..2....0..3..2....0..1..0....0..0..3....0..0..0
..3..0..0....1..2..0....0..0..1....0..0..1....3..2..0....0..1..2....1..2..3

Crossrefs

Row 2 is A033996(n-1)

Sequence in context: A197285 A357017 A352672 * A187286 A187189 A021248

Adjacent sequences: A188144 A188145 A188146 * A188148 A188149 A188150

Keyword

nonn,tabl

Author

R. H. Hardin Mar 22 2011

Status

approved