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A299097 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 73, 41, 41, 73, 32, 64, 157, 101, 125, 101, 157, 64, 128, 353, 242, 574, 574, 242, 353, 128, 256, 869, 578, 1847, 2828, 1847, 578, 869, 256, 512, 1993, 1385, 6007, 9624, 9624, 6007, 1385, 1993, 512, 1024, 4557 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

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

...4...13...20....41....101.....242.......578.......1385........3368

...8...29...41...125....574....1847......6007......22330.......78424

..16...73..101...574...2828....9624.....44936.....204059......865754

..32..157..242..1847...9624...42012....255009....1414647.....7786685

..64..353..578..6007..44936..255009...2170819...16528508...123272050

.128..869.1385.22330.204059.1414647..16528508..161247816..1570964262

.256.1993.3368.78424.865754.7786685.123272050.1570964262.20536604982

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 16] for n>17

k=4: [order 68] for n>69

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A298215.

Sequence in context: A299948 A298221 A299350 * A299879 A299015 A299806

Adjacent sequences:  A299094 A299095 A299096 * A299098 A299099 A299100

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 02 2018

STATUS

approved

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Last modified October 16 19:39 EDT 2021. Contains 348044 sequences. (Running on oeis4.)