A302415 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 17, 25, 8, 16, 37, 30, 81, 16, 32, 78, 66, 120, 264, 32, 64, 169, 142, 259, 441, 857, 64, 128, 361, 289, 698, 994, 1431, 2785, 128, 256, 778, 599, 1650, 3553, 3548, 4754, 9050, 256, 512, 1673, 1268, 3655, 11998, 16123, 12442, 16423, 29407, 512, 1024

Offset

1,2

Comments

Table starts

...1.....2.....4......8......16.......32........64........128.........256

...2.....8....17.....37......78......169.......361........778........1673

...4....25....30.....66.....142......289.......599.......1268........2660

...8....81...120....259.....698.....1650......3655.......8544.......20246

..16...264...441....994....3553....11998.....33596......98387......295578

..32...857..1431...3548...16123....84581....306064....1137414.....4669030

..64..2785..4754..12442...69537...518736...2342685...10963076....58365289

.128..9050.16423..46066..318944..3464956..20184979..119713006...845708279

.256.29407.55848.166341.1443006.23154338.170625048.1280996808.12137387233

Links

R. H. Hardin, Table of n, a(n) for n = 1..288

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 31] for n>33

k=5: [order 66] for n>73

Empirical for row n:

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

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

n=3: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) for n>9

n=4: [order 16] for n>21

n=5: [order 31] for n>39

n=6: [order 79] for n>86

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240478.

Row 1 is A000079(n-1).

Row 2 is A281470.

Sequence in context: A339490 A281469 A302623 * A303182 A302322 A303016

Adjacent sequences: A302412 A302413 A302414 * A302416 A302417 A302418

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 07 2018

Status

approved