A268327 T(n,k)=Number of length-(n+1) 0..k arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

2, 2, 3, 2, 4, 6, 2, 4, 10, 11, 2, 4, 11, 25, 22, 2, 4, 11, 32, 66, 43, 2, 4, 11, 33, 102, 177, 86, 2, 4, 11, 33, 113, 337, 485, 171, 2, 4, 11, 33, 114, 418, 1148, 1348, 342, 2, 4, 11, 33, 114, 434, 1644, 3984, 3797, 683, 2, 4, 11, 33, 114, 435, 1806, 6729, 14030, 10812, 1366, 2, 4

Offset

1,1

Comments

Table starts

...2.....2.....2......2......2......2......2......2......2......2......2......2

...3.....4.....4......4......4......4......4......4......4......4......4......4

...6....10....11.....11.....11.....11.....11.....11.....11.....11.....11.....11

..11....25....32.....33.....33.....33.....33.....33.....33.....33.....33.....33

..22....66...102....113....114....114....114....114....114....114....114....114

..43...177...337....418....434....435....435....435....435....435....435....435

..86...485..1148...1644...1806...1828...1829...1829...1829...1829...1829...1829

.171..1348..3984...6729...8052...8347...8376...8377...8377...8377...8377...8377

.342..3797.14030..28306..37851..40967..41466..41503..41504..41504..41504..41504

.683.10812.49973.121290.184910.213476.220115.220911.220957.220958.220958.220958

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -14*a(n-2) +21*a(n-4) -7*a(n-5) -6*a(n-6)

k=3: [order 12]

k=4: [order 19]

k=5: [order 29]

k=6: [order 40]

k=7: [order 54]

Example

Some solutions for n=9 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....0....1....1....1....0....1....0....1....1....1....1....0
..2....1....0....2....0....2....2....2....1....2....0....2....2....2....2....1
..0....1....0....0....0....0....3....1....1....3....1....3....3....0....0....1
..2....2....2....0....1....2....0....2....2....1....0....0....1....3....3....2
..0....2....0....1....2....3....1....3....3....3....2....4....2....2....0....2
..1....3....3....3....3....1....0....0....4....2....1....3....4....0....0....0
..0....1....0....1....1....0....0....1....1....0....0....1....2....2....0....3
..1....1....1....0....2....1....0....3....4....1....1....4....3....4....1....1
..2....0....2....3....3....2....2....4....3....2....1....2....0....2....0....4

Crossrefs

Column 1 is A005578(n+1).

Sequence in context: A305811 A239471 A241509 * A053023 A153725 A102247

Adjacent sequences: A268324 A268325 A268326 * A268328 A268329 A268330

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 01 2016

Status

approved