A298547 - OEIS

A298547

T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 109, 61, 3, 5, 216, 588, 588, 216, 5, 8, 793, 3276, 4771, 3276, 793, 8, 13, 2907, 18500, 41762, 41762, 18500, 2907, 13, 21, 10622, 104034, 367315, 575754, 367315, 104034, 10622, 21, 34, 38809, 585134, 3215618, 7967553

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OFFSET

1,5

COMMENTS

Table starts

..0.....1.......1.........2...........3.............5...............8

..1.....4......17........61.........216...........793............2907

..1....17.....109.......588........3276.........18500..........104034

..2....61.....588......4771.......41762........367315.........3215618

..3...216....3276.....41762......575754.......7967553.......109775311

..5...793...18500....367315.....7967553.....173576070......3761355239

..8..2907..104034...3215618...109775311....3761355239....128132389259

.13.10622..585134..28178880..1514903717...81677753297...4376310739604

.21.38809.3291766.246983338.20908710812.1774108927621.149522986489383

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

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

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

k=3: [order 12] for n>13

k=4: [order 36] for n>39

EXAMPLE

Some solutions for n=6 k=4

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297917.

Sequence in context: A298653 A299607 A297923 * A298337 A299398 A299228

Adjacent sequences: A298544 A298545 A298546 * A298548 A298549 A298550

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 21 2018

STATUS

approved