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A187162 T(n,k) = Number of n-step self-avoiding walks on a k X k X k 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

Cf. A187163, A187164, A187165, A187166, A187167, A187168, A187169, A187170, A187171.

Sequence in context: A088663 A291681 A011997 * A197618 A340953 A047771

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 November 29 11:46 EST 2021. Contains 349416 sequences. (Running on oeis4.)