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A316615 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 5
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 14, 21, 8, 13, 53, 28, 28, 53, 13, 21, 105, 63, 77, 63, 105, 21, 34, 237, 126, 199, 199, 126, 237, 34, 55, 577, 245, 454, 649, 454, 245, 577, 55, 89, 1205, 505, 1074, 1749, 1749, 1074, 505, 1205, 89, 144, 2681, 1037, 2619, 4719, 5464 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2....3....5.....8.....13.....21......34.......55........89.......144

..2....5....9...21....53....105....237.....577.....1205......2681......6349

..3....9...14...28....63....126....245.....505.....1037......2088......4230

..5...21...28...77...199....454...1074....2619.....6216.....14782.....35494

..8...53...63..199...649...1749...4719...13770....38535....106694....302759

.13..105..126..454..1749...5464..17224...58861...190509....613009...2033562

.21..237..245.1074..4719..17224..65158..261426...990387...3768844..14720334

.34..577..505.2619.13770..58861.261426.1249304..5600646..25176200.116672242

.55.1205.1037.6216.38535.190509.990387.5600646.29420195.155127330.847493564

LINKS

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

FORMULA

Empirical for column k:

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

k=2: a(n) = a(n-1) +8*a(n-3) -4*a(n-4)

k=3: [order 12]

k=4: [order 36] for n>37

k=5: [order 40] for n>51

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..0..0..0

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1

..0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..0

..0..0..1..0. .0..0..0..0. .1..1..0..0. .1..0..0..0. .0..0..0..0

..0..0..0..0. .1..0..0..0. .1..1..1..0. .0..0..0..0. .1..0..0..0

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303963.

Column 3 is A305342.

Column 4 is A305343.

Sequence in context: A305649 A316925 A305347 * A316427 A317429 A316239

Adjacent sequences:  A316612 A316613 A316614 * A316616 A316617 A316618

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 08 2018

STATUS

approved

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)