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A304669 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 53, 30, 30, 53, 13, 21, 105, 66, 93, 66, 105, 21, 34, 237, 123, 249, 249, 123, 237, 34, 55, 577, 252, 544, 832, 544, 252, 577, 55, 89, 1205, 535, 1366, 1926, 1926, 1366, 535, 1205, 89, 144, 2681, 1074, 3399, 5311, 5101 (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...13...30....66....123....252.....535....1074.....2194......4530

..5...21...30...93...249....544...1366....3399....8219....20292.....49933

..8...53...66..249...832...1926...5311...15604...41101...113581....322499

.13..105..123..544..1926...5101..15421...48922..143214...444335...1400682

.21..237..252.1366..5311..15421..49516..163216..516865..1750074...5929076

.34..577..535.3399.15604..48922.163216..597306.2045830..7480857..28310502

.55.1205.1074.8219.41101.143214.516865.2045830.7738947.31691371.133498110

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..264

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: a(n) = a(n-1) +4*a(n-3) +2*a(n-5) -a(n-7) -2*a(n-9) -2*a(n-11) -a(n-12)

k=4: [order 42] for n>43

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303963.

Sequence in context: A199512 A303969 A304931 * A306172 A304355 A305918

Adjacent sequences:  A304666 A304667 A304668 * A304670 A304671 A304672

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 16 2018

STATUS

approved

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Last modified August 8 10:26 EDT 2022. Contains 356009 sequences. (Running on oeis4.)