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

Author

R. H. Hardin, Feb 01 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A005578(n+1).

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]