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A187162 T(n,k)=Number of n-step self-avoiding walks on a kXkXk cube summed over all starting positions 10
1, 8, 0, 27, 24, 0, 64, 108, 48, 0, 125, 288, 342, 96, 0, 216, 600, 1056, 1104, 144, 0, 343, 1080, 2370, 3984, 3240, 240, 0, 512, 1764, 4464, 9612, 14256, 9504, 192, 0, 729, 2688, 7518, 18888, 37470, 51504, 25344, 144, 0, 1000, 3888, 11712, 32712, 77184, 148224 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

.1...8.....27......64......125......216.......343.......512.......729......1000

.0..24....108.....288......600.....1080......1764......2688......3888......5400

.0..48....342....1056.....2370.....4464......7518.....11712.....17226.....24240

.0..96...1104....3984.....9612....18888.....32712.....51984.....77604....110472

.0.144...3240...14256....37470....77184....137754....223536....338886....488160

.0.240...9504...51504...148224...320328....588924....975216...1500408...2185704

.0.192..25344..177120...568248..1298016...2466510...4175136...6525450...9619008

.0.144..67824..608928..2188608..5299056..10416624..18026640..28617228..42676728

.0...0.167016.2013360..8227752.21274896..43422072..76964016.124223214.187527168

.0...0.414912.6654048.30938640.85654320.181790352.330218544.541990896.828222216

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical: a(1,k) = k^3

Empirical: a(2,k) = 6*k^3 - 6*k^2

Empirical: a(3,k) = 30*k^3 - 60*k^2 + 24*k for k>1

Empirical: a(4,k) = 150*k^3 - 426*k^2 + 312*k - 48 for k>2

Empirical: a(5,k) = 726*k^3 - 2640*k^2 + 2688*k - 720 for k>3

Empirical: a(6,k) = 3534*k^3 - 15366*k^2 + 19536*k - 7056 for k>4

Empirical: a(7,k) = 16926*k^3 - 85380*k^2 + 128832*k - 57312 for k>5

Empirical: a(8,k) = 81390*k^3 - 463074*k^2 + 801216*k - 418032 for k>6

Empirical: a(9,k) = 387966*k^3 - 2452704*k^2 + 4766544*k - 2833872 for k>7

Empirical: a(10,k) = 1853886*k^3 - 12825630*k^2 + 27515184*k - 18252624 for k>8

EXAMPLE

Solution for n=9 3X3X3

..0..0..0.....9..0..0.....8..0..0

..0..2..1.....6..0..0.....7..0..0

..0..3..0.....5..4..0.....0..0..0

CROSSREFS

Sequence in context: A028604 A088663 A011997 * A197618 A047771 A137528

Adjacent sequences:  A187159 A187160 A187161 * A187163 A187164 A187165

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 06 2011

STATUS

approved

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Last modified May 28 20:12 EDT 2017. Contains 287241 sequences.