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

Author

R. H. Hardin Mar 22 2011

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 2 is A033996(n-1)

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