A302472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1147, 361, 0, 13, 1934, 4556, 10264, 8493, 5486, 1172, 0, 21, 6861, 21843, 78679, 101109, 53575, 25599, 3809, 0, 34, 24386, 103319, 584333, 1141147, 990266, 331044

Offset

1,5

Comments

Table starts

.0.....1......1........2.........3...........5.............8..............13

.0.....3.....14.......45.......146.........537..........1934............6861

.0....11.....49......203.......955........4556.........21843..........103319

.0....34....250.....1401.....10264.......78679........584333.........4330427

.0...111...1147.....8493....101109.....1141147......12546601.......139759054

.0...361...5486....53575....990266....16983273.....278275383......4682106140

.0..1172..25599...331044...9731423...251512646....6145486847....156721340433

.0..3809.121626..2075845..96648626..3770915891..137317050228...5300304476103

.0.12377.572657.12918219.950374395.55956081186.3037409718914.177368160967073

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)

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

k=3: [order 14]

k=4: [order 43] for n>44

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6

n=3: [order 19] for n>21

n=4: [order 63] for n>66

Example

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A302225.

Sequence in context: A319501 A302224 A302670 * A303254 A256068 A302381

Adjacent sequences: A302469 A302470 A302471 * A302473 A302474 A302475

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 08 2018

Status

approved