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A263519
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T(n,k) = Number of (n+1) X (k+1) arrays of permutations of 0..(n+1)*(k+1)-1 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.
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14
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3, 7, 8, 15, 35, 23, 29, 160, 208, 66, 53, 660, 2076, 1198, 190, 93, 2651, 18369, 25968, 7022, 547, 159, 10350, 158109, 489294, 331130, 41035, 1575, 267, 39807, 1317780, 9051857, 13332096, 4213002, 240237, 4535, 443, 151463, 10791350, 162207955
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OFFSET
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1,1
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COMMENTS
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Table starts
.....3.......7.........15............29...............53..................93
.....8......35........160...........660.............2651...............10350
....23.....208.......2076.........18369...........158109.............1317780
....66....1198......25968........489294..........9051857...........162207955
...190....7022.....331130......13332096........529329240.........20339400914
...547...41035....4213002.....362159570......30867389241.......2543460828164
..1575..240237...53712998....9866744449....1805523575884.....319022980139204
..4535.1406038..684799391..268827612021..105637731091773...40028581755172441
.13058.8230727.8732881192.7327820172316.6184312882582853.5025951440933512579
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) -a(n-3)
k=2: [order 10]
k=3: [order 35]
Empirical for row n:
n=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)
n=2: [order 10]
n=3: [order 29]
n=4: [order 92]
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..7..8..9....0..1..7..8..9....0..1..2..3..4....0..1..2..4..9
..6..5..2..3..4...10..5..2..3..4....5..6..8..7..9....5..7..6..3..8
.10.12.11.13.19...11..6.12.13.14...15.10.13.12.14...10.12.11.14.13
.15.17.16.18.14...15.16.17.19.18...16.11.18.17.19...15.16.17.18.19
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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