A302278 T(n,k) = number of n X k 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 22, 23, 0, 5, 27, 29, 79, 61, 0, 8, 45, 74, 89, 269, 162, 0, 13, 98, 162, 283, 353, 942, 421, 0, 21, 193, 363, 649, 1219, 941, 3401, 1103, 0, 34, 379, 782, 1621, 3621, 3854, 3316, 12283, 2890, 0, 55, 778, 1766, 4209, 14125, 15862, 14639

Offset: 1

Author

R. H. Hardin, Apr 04 2018

Keywords

• nonn
• tabl

Comments

Table starts

0 1 1 2 3 5 8 13 21 34

0 3 7 10 27 45 98 193 379 778

0 10 22 29 74 162 363 782 1766 3953

0 23 79 89 283 649 1621 4209 9563 25179

0 61 269 353 1219 3621 14125 38410 108141 360173

0 162 942 941 3854 15862 72083 229708 713848 2948380

0 421 3401 3316 14639 69601 384916 1354563 4386347 20677591

0 1103 12283 12016 63093 385242 3027442 11370253 43394297 258471515

0 2890 43006 34060 222254 1809350 17837758 75667277 325745362 2460590443

Examples

			Some solutions for n=5, k=4:
  0 0 1 1     0 1 1 1     0 0 0 0     0 0 0 0     0 0 1 0
  1 1 0 0     0 0 1 0     1 1 1 1     0 1 0 1     1 1 0 0
  1 0 1 0     0 0 0 0     0 1 0 1     1 0 1 0     0 0 0 1
  1 0 1 0     0 1 1 1     1 0 1 0     1 1 1 1     0 1 1 1
  0 1 0 1     1 0 0 0     0 1 0 1     0 0 0 0     1 1 0 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 2 is A185828.

Row 1 is A000045(n-1).

Formula

Empirical for column k:

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

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

k=3: [order 18]

k=4: [order 72] for n > 73

Empirical for row n:

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

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

n=3: [order 16] for n > 18

n=4: [order 64] for n > 66