A299350 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 8 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, 73, 40, 40, 73, 32, 64, 157, 89, 120, 89, 157, 64, 128, 353, 195, 503, 503, 195, 353, 128, 256, 869, 451, 1492, 2067, 1492, 451, 869, 256, 512, 1993, 1046, 4767, 6605, 6605, 4767, 1046, 1993, 512, 1024, 4557, 2453

Offset

1,2

Comments

Table starts

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

...2....7...13....29.....73.....157......353.......869.......1993........4557

...4...13...20....40.....89.....195......451......1046.......2453........5810

...8...29...40...120....503....1492.....4767.....17127......56292......185937

..16...73...89...503...2067....6605....30814....125890.....498977.....2155139

..32..157..195..1492...6605...25754...150748....749550....3771027....20403891

..64..353..451..4767..30814..150748..1262771...8560581...57300258...426035059

.128..869.1046.17127.125890..749550..8560581..72445170..624861384..6151095307

.256.1993.2453.56292.498977.3771027.57300258.624861384.7208056818.93531514754

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6

k=3: [order 14] for n>15

k=4: [order 62] for n>65

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298215.

Column 3 is A298216.

Column 4 is A298217.

Sequence in context: A299187 A299948 A298221 * A299097 A299879 A299015

Adjacent sequences: A299347 A299348 A299349 * A299351 A299352 A299353

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 07 2018

Status

approved