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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 12:12 EST 2022. Contains 358656 sequences. (Running on oeis4.)