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A298337 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 113, 61, 3, 5, 216, 628, 628, 216, 5, 8, 793, 3641, 5663, 3641, 793, 8, 13, 2907, 21375, 51588, 51588, 21375, 2907, 13, 21, 10622, 124972, 479767, 755110, 479767, 124972, 10622, 21, 34, 38809, 730509, 4442111, 11244900 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

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

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

..1....17.....113.......628........3641.........21375..........124972

..2....61.....628......5663.......51588........479767.........4442111

..3...216....3641.....51588......755110......11244900.......166636876

..5...793...21375....479767....11244900.....268494008......6373591375

..8..2907..124972...4442111...166636876....6373591375....242019919082

.13.10622..730509..41117169..2469362361..151336485128...9195408207604

.21.38809.4271331.380674402.36605480121.3595159432175.349596064308984

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 13] for n>15

k=4: [order 48] for n>50

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297917.

Sequence in context: A299607 A297923 A298547 * A299398 A299228 A300040

Adjacent sequences:  A298334 A298335 A298336 * A298338 A298339 A298340

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 17 2018

STATUS

approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)