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A264071 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 0,1 or 1,2. 11
2, 5, 4, 13, 21, 8, 34, 121, 89, 16, 89, 605, 1210, 377, 32, 233, 3025, 12100, 12100, 1597, 64, 610, 15125, 131890, 239580, 121000, 6765, 128, 1597, 75625, 1445345, 5645376, 4745620, 1210000, 28657, 256, 4181, 378125, 15892745, 130697424, 242621698 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....2.......5..........13.............34................89..................233

....4......21.........121............605..............3025................15125

....8......89........1210..........12100............131890..............1445345

...16.....377.......12100.........239580...........5645376............130697424

...32....1597......121000........4745620.........242621698..........11909009849

...64....6765.....1210000.......94000060.......10427064769........1084282319384

..128...28657....12100000.....1861931060......448121165789.......98725402363225

..256..121393...121000000....36880691100....19258783041289.....8989061417123964

..512..514229..1210000000...730524027860...827679549612058...818464496640651553

.1024.2178309.12100000000.14470047586940.35570961850254336.74522143720797473932

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..143

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) for n>2

k=4: a(n) = 19*a(n-1) +16*a(n-2) for n>3

k=5: a(n) = 43*a(n-1) -43*a(n-3) +a(n-4) for n>5

k=6: a(n) = 87*a(n-1) +374*a(n-2) -470*a(n-3) +207*a(n-4) +3*a(n-5) for n>7

k=7: a(n) = 191*a(n-1) +1102*a(n-2) -7594*a(n-3) -38349*a(n-4) +38507*a(n-5) for n>8

Empirical for row n:

n=1: a(n) = 3*a(n-1) -a(n-2)

n=2: a(n) = 5*a(n-1) for n>3

n=3: a(n) = 12*a(n-1) -12*a(n-2) +12*a(n-3) -12*a(n-4) +a(n-5) for n>7

n=4: a(n) = 24*a(n-1) -19*a(n-2) -11*a(n-3) +36*a(n-4) +3*a(n-5) for n>9

n=5: [order 14] for n>19

n=6: [order 10] for n>19

EXAMPLE

Some solutions for n=3 k=4

..0..8..9..3..4....6..1..2..3..4....7..8..2..3..4....0..8..2..3..4

..5.13..7..1..2...11.13..0..8..9...12..6..0..1..9....5..6..7..1..9

.16.11.18..6.14...10..5.19..7.14...17..5.18.13.14...17.18.12.13.14

.15.10.17.12.19...15.16.17.18.12...15.16.10.11.19...15.16.10.11.19

CROSSREFS

Column 1 is A000079.

Column 2 is A015448(n+1).

Row 1 is A001519(n+1).

Sequence in context: A080067 A117824 A122212 * A212188 A331213 A298585

Adjacent sequences:  A264068 A264069 A264070 * A264072 A264073 A264074

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 02 2015

STATUS

approved

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)