A268049 T(n,k)=Number of nXk 0..k arrays with every repeated value in every row unequal to, and in every column equal to, the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 4, 14, 4, 12, 159, 122, 7, 40, 3183, 9054, 938, 12, 154, 88243, 1650058, 467899, 6734, 20, 656, 3222467, 525124941, 829256141, 22309009, 45938, 33, 3074, 147078491, 262999737747, 3273871468927, 386602239495, 999810316, 302402, 54

Offset

1,2

Comments

Table starts

..1.......2...........4..............12................40...............154

..2......14.........159............3183.............88243...........3222467

..4.....122........9054.........1650058.........525124941......262999737747

..7.....938......467899.......829256141.....3273871468927.24754240745963975

.12....6734....22309009....386602239495.19146833412153174

.20...45938...999810316.168939588471080

.33..302402.42764566838

.54.1939154

.88

Links

R. H. Hardin, Table of n, a(n) for n = 1..48

Formula

Empirical for column k:

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

k=2: a(n) = 14*a(n-1) -60*a(n-2) +50*a(n-3) +145*a(n-4) -80*a(n-5) -84*a(n-6) +16*a(n-7)

k=3: [order 78]

Example

Some solutions for n=5 k=4
..0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0....0..0..1..0
..0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0....0..1..0..0
..2..0..0..1....2..1..0..3....1..0..0..1....1..1..0..2....2..0..0..3
..3..0..0..2....4..0..0..4....0..2..0..3....0..1..0..3....4..4..0..1
..4..2..4..1....3..2..0..1....0..2..0..1....3..4..0..2....1..1..3..0

Crossrefs

Column 1 is A000071(n+2).

Column 2 is A267906.

Row 1 is A268010.

Row 2 is A268011.

Sequence in context: A204978 A204705 A206650 * A267911 A120654 A121514

Adjacent sequences: A268046 A268047 A268048 * A268050 A268051 A268052

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2016

Status

approved