A280604 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 45, 50, 16, 32, 138, 116, 116, 138, 32, 64, 383, 293, 302, 293, 383, 64, 128, 1063, 735, 726, 726, 735, 1063, 128, 256, 2951, 1844, 1709, 1648, 1709, 1844, 2951, 256, 512, 8193, 4626, 3996, 3647, 3647, 3996, 4626, 8193, 512

Offset

1,2

Comments

Table starts

...1.....2.....4.....8....16.....32.....64....128....256.....512....1024

...2.....7....18....50...138....383...1063...2951...8193...22748...63161

...4....18....45...116...293....735...1844...4626..11611...29151...73200

...8....50...116...302...726...1709...3996...9346..21891...51367..120680

..16...138...293...726..1648...3647...8031..17745..39427...87996..197061

..32...383...735..1709..3647...7594..15792..33136..70293..150510..324417

..64..1063..1844..3996..8031..15792..31152..62349.126893..261994..546766

.128..2951..4626..9346.17745..33136..62349.119656.234789..469715..953647

.256..8193.11611.21891.39427..70293.126893.234789.446500..869877.1726530

.512.22748.29151.51367.87996.150510.261994.469715.869877.1658080.3232058

Links

R. H. Hardin, Table of n, a(n) for n = 1..510

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-5) -3*a(n-7) +2*a(n-8) +a(n-9) -a(n-10) for n>13

k=5: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-6) -2*a(n-7) -3*a(n-8) +5*a(n-9) -a(n-10) -a(n-11) -a(n-12) +a(n-13) for n>15

k=6: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-7) -2*a(n-8) -3*a(n-9) +5*a(n-10) -a(n-11) -a(n-12) -a(n-14) +a(n-15) for n>19

k=7: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) +2*a(n-8) -2*a(n-9) -3*a(n-10) +5*a(n-11) -a(n-12) -a(n-13) -a(n-16) +a(n-17) for n>22

Example

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

Crossrefs

Column 1 is A000079(n-1).

Sequence in context: A299806 A299682 A300314 * A301323 A300498 A300937

Adjacent sequences: A280601 A280602 A280603 * A280605 A280606 A280607

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2017

Status

approved