A298494 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 27, 27, 69, 32, 64, 137, 43, 41, 43, 137, 64, 128, 301, 70, 101, 101, 70, 301, 128, 256, 705, 106, 158, 178, 158, 106, 705, 256, 512, 1461, 169, 263, 253, 253, 263, 169, 1461, 512, 1024, 3193, 276, 481, 423, 388

Offset

1,2

Comments

Table starts

...1....2...4...8...16...32...64..128..256..512.1024..2048..4096..8192..16384

...2....7..13..29...69..137..301..705.1461.3193.7373.15729.34405.78569.170813

...4...13..20..27...43...70..106..169..276..444..720..1183..1947..3207...5311

...8...29..27..41..101..158..263..481..776.1387.2567..4539..8077.14329..25589

..16...69..43.101..178..253..423..715.1082.1821.3203..5330..8978.15692..26461

..32..137..70.158..253..388..434..830.1351.1892.3026..5492..8206.13206..23026

..64..301.106.263..423..434..628.1067.1267.1943.2973..4583..6623.10201..15735

.128..705.169.481..715..830.1067.1708.2118.2978.4984..7136.10725.17602..27551

.256.1461.276.776.1082.1351.1267.2118.2860.3333.5106..7796.10253.15979..24788

Links

R. H. Hardin, Table of n, a(n) for n = 1..1010

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6

k=3: [order 11] for n>12

k=4: [order 41] for n>43

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A297883.

Sequence in context: A297889 A298294 A299388 * A299187 A299948 A298221

Adjacent sequences: A298491 A298492 A298493 * A298495 A298496 A298497

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 20 2018

Status

approved