A245163 T(n,k)=Number of length n 0..k arrays with new values introduced in order from both ends.

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 4, 8, 1, 1, 2, 4, 9, 16, 1, 1, 2, 4, 9, 23, 32, 1, 1, 2, 4, 9, 23, 64, 64, 1, 1, 2, 4, 9, 23, 65, 186, 128, 1, 1, 2, 4, 9, 23, 65, 199, 551, 256, 1, 1, 2, 4, 9, 23, 65, 199, 653, 1645, 512, 1, 1, 2, 4, 9, 23, 65, 199, 654, 2275, 4926, 1024, 1, 1, 2, 4, 9, 23

Offset: 1

Author

R. H. Hardin, Jul 12 2014

Keywords

• nonn
• tabl

Comments

Table starts

.....1........1.........1.........1.........1.........1.........1.........1

.....1........1.........1.........1.........1.........1.........1.........1

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

.....4........4.........4.........4.........4.........4.........4.........4

.....8........9.........9.........9.........9.........9.........9.........9

....16.......23........23........23........23........23........23........23

....32.......64........65........65........65........65........65........65

....64......186.......199.......199.......199.......199.......199.......199

...128......551.......653.......654.......654.......654.......654.......654

...256.....1645......2275......2296......2296......2296......2296......2296

...512.....4926......8313......8568......8569......8569......8569......8569

..1024....14768.....31439.....33794.....33825.....33825.....33825.....33825

..2048....44293....121637....140039....140580....140581....140581....140581

..4096...132867....477307....605869....612890....612933....612933....612933

..8192...398588...1888721...2718531...2794159...2795181...2795182...2795182

.16384..1195750...7509799..12564289..13280627..13298407..13298464..13298464

.32768..3587235..29940861..59419764..65597882..65851100..65852872..65852873

.65536.10761689.119550419.285878342.335521900.338654554.338694406.338694479

Examples

			Some solutions for n=10 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....0....1....0....1....0....1....1....0....0....1....1....0
..1....0....2....0....1....2....1....0....0....2....2....0....1....1....2....1
..0....1....3....1....2....0....0....2....0....2....1....1....0....1....2....0
..1....2....0....0....0....1....2....3....0....3....1....2....1....1....2....1
..0....2....0....2....2....1....0....3....1....1....0....1....2....2....2....0
..0....1....2....1....2....1....0....2....1....3....2....1....1....1....1....2
..0....1....1....2....1....1....1....0....1....2....1....1....1....2....1....1
..1....1....1....1....1....1....0....1....0....1....1....0....1....1....1....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
		

Links

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

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A164039(n-2)

Diagonal is A007476

Formula

Empirical for column k:

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

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

k=3: a(n) = 10*a(n-1) -37*a(n-2) +64*a(n-3) -52*a(n-4) +16*a(n-5) for n>6

k=4: [order 7] for n>8

k=5: [order 9] for n>10

k=6: [order 11] for n>12

k=7: [order 13] for n>14