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A304544 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 35, 19, 19, 35, 13, 21, 61, 37, 70, 37, 61, 21, 34, 127, 65, 124, 124, 65, 127, 34, 55, 265, 129, 328, 461, 328, 129, 265, 55, 89, 507, 275, 808, 949, 949, 808, 275, 507, 89, 144, 1013, 555, 2265, 2792, 2558, 2792, 2265 (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...7...17....35.....61.....127......265......507......1013.......2071

..3...7...9...19....37.....65.....129......275......555......1143.......2417

..5..17..19...70...124....328.....808.....2265.....6025.....17221......50786

..8..35..37..124...461....949....2792....10838....31286....102740.....377657

.13..61..65..328...949...2558....9840....40134...152679....664967....2951738

.21.127.129..808..2792...9840...53098...285622..1415123...8070788...46626298

.34.265.275.2265.10838..40134..285622..1991764.12087446..88143119..641080685

.55.507.555.6025.31286.152679.1415123.12087446.96472384.894904467.8247056696

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..219

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 13]

k=4: [order 67] for n>68

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A304133 A303808 A304855 * A306129 A304221 A305482

Adjacent sequences:  A304541 A304542 A304543 * A304545 A304546 A304547

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, May 14 2018

STATUS

approved

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Last modified May 23 08:14 EDT 2022. Contains 353961 sequences. (Running on oeis4.)