

A188147


T(n,k)=Number of nstep selfavoiding 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
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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(n1)
Sequence in context: A245638 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



