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

1,6

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

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) 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

Example

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

Crossrefs

Column 1 is A000079(n-2)

Column 2 is A164039(n-2)

Diagonal is A007476

Sequence in context: A141021 A140995 A140994 * A140993 A027935 A137940

Adjacent sequences: A245160 A245161 A245162 * A245164 A245165 A245166

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 12 2014

Status

approved