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A264244 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 1,1 0,-1 -1,1 or 0,-2. 13
2, 8, 3, 21, 21, 5, 57, 95, 89, 8, 164, 557, 804, 296, 13, 460, 3303, 9005, 5055, 1105, 21, 1289, 18725, 108020, 119737, 36193, 3897, 34, 3629, 105839, 1249237, 2982248, 1696877, 243881, 14128, 55, 10202, 602365, 14586353, 70618408, 86191713 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2......8.......21..........57............164.............460.............1289

..3.....21.......95.........557...........3303...........18725...........105839

..5.....89......804........9005.........108020.........1249237.........14586353

..8....296.....5055......119737........2982248........70618408.......1687935233

.13...1105....36193.....1696877.......86191713......4157973485.....203949869341

.21...3897...243881....23471441.....2448948509....240749059561...24147725322385

.34..14128..1688581...327315125....69880683436..13986284450284.2870671705359089

.55..50533.11546272..4550623993..1990480615856.810930428170425

.89.181937.79399773.63332634829.56719203638885

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..97

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +6*a(n-2) -a(n-3)

k=3: a(n) = 7*a(n-1) +7*a(n-2) -65*a(n-3) +65*a(n-4) +62*a(n-5) -72*a(n-6)

k=4: [order 18]

k=5: [order 48]

Empirical for row n:

n=1: a(n)=2*a(n-1)+a(n-2)+4*a(n-3)-a(n-4)-a(n-6)

n=2: [order 9] for n>10

EXAMPLE

Some solutions for n=4 k=4

..1..5..2..3..4....1..5..2..7..4....1..2..6..3..4....0..1..4..3..8

..6..0..7..8..9....6..0..9..8..3....7..0.11..9.13....5..6..9..2.13

.10.12.16.17.14...10.13.12.14.18...10..5.12.14..8...10.11.12..7.14

.15.20.11.19.13...16.20.11.19.23...15.17.21.19.23...17.16.21.18.19

.21.23.22.24.18...21.15.22.17.24...20.22.16.24.18...20.15.22.23.24

CROSSREFS

Column 1 is A000045(n+2).

Sequence in context: A278117 A153188 A193976 * A292930 A126951 A282637

Adjacent sequences:  A264241 A264242 A264243 * A264245 A264246 A264247

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 09 2015

STATUS

approved

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Last modified February 26 03:24 EST 2020. Contains 332272 sequences. (Running on oeis4.)