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A188147 T(n,k)=Number of n-step self-avoiding walks on a kXk square summed over all starting positions 9
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 (list; table; graph; refs; listen; history; text; internal format)
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: A198866 A176220 A197285 * A187286 A187189 A021248

Adjacent sequences:  A188144 A188145 A188146 * A188148 A188149 A188150

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 22 2011

STATUS

approved

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Last modified April 20 16:29 EDT 2014. Contains 240807 sequences.