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A305516 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 5, 1, 3, 5, 8, 6, 6, 8, 5, 8, 5, 8, 10, 8, 5, 8, 13, 22, 19, 13, 13, 19, 22, 13, 21, 29, 33, 38, 62, 38, 33, 29, 21, 34, 60, 60, 73, 108, 108, 73, 60, 60, 34, 55, 121, 107, 164, 353, 343, 353, 164, 107, 121, 55, 89, 194, 204, 351, 982, 925, 925, 982 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0..1...1...2....3....5.....8.....13.....21......34.......55........89

..1..3...2...1....8....5....22.....29.....60.....121......194.......425

..1..2...5...6....8...19....33.....60....107.....204......375.......677

..2..1...6..10...13...38....73....164....351.....749.....1719......3710

..3..8...8..13...62..108...353....982...2362....6902....17966.....48328

..5..5..19..38..108..343...925...2627...7334...20665....56990....159501

..8.22..33..73..353..925..3547..14118..43745..173690...619516...2147913

.13.29..60.164..982.2627.14118..61412.226004.1060302..4311525..17892039

.21.60.107.351.2362.7334.43745.226004.923608.4939048.23169076.107297290

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

FORMULA

Empirical for column k:

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

k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>6

k=3: [order 10] for n>13

k=4: [order 14] for n>17

k=5: [order 45] for n>49

k=6: [order 91] for n>100

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297809 for n>2.

Sequence in context: A225849 A038575 A304302 * A305182 A291047 A033178

Adjacent sequences:  A305513 A305514 A305515 * A305517 A305518 A305519

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 03 2018

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)