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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. 13
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Column 2 is A185828.

Row 1 is A000045(n-1).

Sequence in context: A248820 A085550 A223139 * A302728 A302528 A303410

Adjacent sequences:  A302275 A302276 A302277 * A302279 A302280 A302281

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 04 2018

STATUS

approved

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Last modified August 3 04:30 EDT 2020. Contains 336197 sequences. (Running on oeis4.)