A302278 - OEIS

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.

%I #7 Apr 05 2018 04:09:22

%S 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,

%T 0,13,98,162,283,353,942,421,0,21,193,363,649,1219,941,3401,1103,0,34,

%U 379,782,1621,3621,3854,3316,12283,2890,0,55,778,1766,4209,14125,15862,14639

%N 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.

%C Table starts

%C 0 1 1 2 3 5 8 13 21 34

%C 0 3 7 10 27 45 98 193 379 778

%C 0 10 22 29 74 162 363 782 1766 3953

%C 0 23 79 89 283 649 1621 4209 9563 25179

%C 0 61 269 353 1219 3621 14125 38410 108141 360173

%C 0 162 942 941 3854 15862 72083 229708 713848 2948380

%C 0 421 3401 3316 14639 69601 384916 1354563 4386347 20677591

%C 0 1103 12283 12016 63093 385242 3027442 11370253 43394297 258471515

%C 0 2890 43006 34060 222254 1809350 17837758 75667277 325745362 2460590443

%H R. H. Hardin, <a href="/A302278/b302278.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

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

%F Empirical for row n:

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

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

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

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

%e Some solutions for n=5, k=4:

%e 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0

%e 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0

%e 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1

%e 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1

%e 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0

%Y Column 2 is A185828.

%Y Row 1 is A000045(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 04 2018