login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of (n+2)X4 binary arrays avoiding patterns 001 and 100 in rows, columns and nw-to-se diagonals
1

%I #5 Mar 31 2012 12:36:49

%S 260,943,3906,16595,72124,315526,1386452,6101978,26880779,118462616,

%T 522168918,2301871117,10147794186,44737519502,197231808618,

%U 869529453650,3833476152984,16900586528613,74509397913883,328488719268563

%N Number of (n+2)X4 binary arrays avoiding patterns 001 and 100 in rows, columns and nw-to-se diagonals

%C Column 2 of A202591

%H R. H. Hardin, <a href="/A202585/b202585.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +12*a(n-2) -13*a(n-3) -58*a(n-4) -15*a(n-5) +99*a(n-6) +100*a(n-7) -11*a(n-8) -61*a(n-9) -54*a(n-10) -16*a(n-11) +10*a(n-12) +6*a(n-13) -2*a(n-14) +a(n-16) for n>17

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 21 2011