

A306166


T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 kingmove adjacent elements, with upper left element zero.


7



1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 17, 9, 16, 32, 22, 32, 32, 22, 32, 64, 45, 77, 103, 77, 45, 64, 128, 101, 207, 298, 298, 207, 101, 128, 256, 218, 523, 962, 1188, 962, 523, 218, 256, 512, 477, 1304, 2966, 4849, 4849, 2966, 1304, 477, 512, 1024, 1041, 3307, 8756, 19176
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OFFSET

1,2


COMMENTS

Table starts
...1...2....4.....8.....16......32.......64.......128........256.........512
...2...4....5.....9.....22......45......101.......218........477........1041
...4...5...17....32.....77.....207......523......1304.......3307........8414
...8...9...32...103....298.....962.....2966......8756......26287.......79873
..16..22...77...298...1188....4849....19176.....75681.....302442.....1206813
..32..45..207...962...4849...25226...128710....660871....3402775....17536734
..64.101..523..2966..19176..128710...842280...5553315...36528087...240890311
.128.218.1304..8756..75681..660871..5553315..47632142..405555135..3465256979
.256.477.3307.26287.302442.3402775.36528087.405555135.4469582265.49440451905


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..287


FORMULA

Empirical for column k:
k=1: a(n) = 2*a(n1)
k=2: a(n) = a(n1) +3*a(n2) 2*a(n4) for n>6
k=3: a(n) = a(n1) +2*a(n2) +5*a(n3) +2*a(n4) 2*a(n5) 8*a(n6) 8*a(n7) for n>10
k=4: [order 18] for n>23
k=5: [order 40] for n>47


EXAMPLE

Some solutions for n=5 k=4
..0..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
..1..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..0..0. .1..1..1..1
..0..0..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .1..0..1..1


CROSSREFS

Column 1 is A000079(n1).
Column 2 is A052962 for n>2.
Sequence in context: A304604 A316420 A304926 * A317383 A033717 A320202
Adjacent sequences: A306163 A306164 A306165 * A306167 A306168 A306169


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Jun 23 2018


STATUS

approved



