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A306172 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero. 6
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, 1372, 1956, 1956, 1372, 535, 1205, 89, 144, 2681, 1074, 3411, 5421, 5277 (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...1372....3411.....8269....20472.....50397

..8...53...66..249...832...1956...5421...15993....42682...118773....341634

.13..105..123..544..1956...5277..16195...52752...158458...503426...1626380

.21..237..252.1372..5421..16195..53834..185090...619073..2213741...7903854

.34..577..535.3411.15993..52752.185090..722779..2706166.10841923..44886700

.55.1205.1074.8269.42682.158458.619073.2706166.11592019.54162509.259464240

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

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 40] for n>41

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303963.

Column 3 is A304664.

Sequence in context: A303969 A304931 A304669 * A304355 A305918 A305649

Adjacent sequences:  A306169 A306170 A306171 * A306173 A306174 A306175

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 23 2018

STATUS

approved

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Last modified January 17 17:47 EST 2022. Contains 350402 sequences. (Running on oeis4.)