A304926 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 15, 9, 16, 32, 22, 31, 31, 22, 32, 64, 45, 73, 87, 73, 45, 64, 128, 101, 191, 266, 266, 191, 101, 128, 256, 218, 466, 851, 1054, 851, 466, 218, 256, 512, 477, 1125, 2510, 4186, 4186, 2510, 1125, 477, 512, 1024, 1041, 2762, 7348, 16158

Offset

1,2

Comments

Table starts

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

...2...4....5.....9.....22......45......101.......218........477........1041

...4...5...15....31.....73.....191......466......1125.......2762........6805

...8...9...31....87....266.....851.....2510......7348......21910.......65581

..16..22...73...266...1054....4186....16158.....63555.....251536......988178

..32..45..191...851...4186...21214...104451....524286....2629697....13159898

..64.101..466..2510..16158..104451...649029...4123792...26044218...164807242

.128.218.1125..7348..63555..524286..4123792..33757130..273455401..2220694647

.256.477.2762.21910.251536.2629697.26044218.273455401.2831764125.29378878160

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>9

k=4: [order 13] for n>18

k=5: [order 34] for n>41

k=6: [order 96] for n>103

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..1..1
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..0. .1..1..1..1
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .1..1..1..0
..0..0..1..0. .0..0..0..1. .0..0..1..0. .0..1..0..0. .1..0..1..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A305340 A304604 A316420 * A306166 A317383 A033717

Adjacent sequences: A304923 A304924 A304925 * A304927 A304928 A304929

Keyword

nonn,tabl

Author

R. H. Hardin, May 21 2018

Status

approved