%I #5 Mar 31 2012 12:36:44
%S 3,14,47,191,752,2732,9111,28011,79918,213153,535318,1274359,2892516,
%T 6291669,13172108,26642251,52229342,99517435,184747946,334871408,
%U 593751872,1031516926,1758440929,2945277335,4852655894,7873078897
%N Number of nX4 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor
%C Column 4 of A201353
%H R. H. Hardin, <a href="/A201349/b201349.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/1307674368000)*n^15 - (1/87178291200)*n^14 + (19/7472424960)*n^13 - (61/958003200)*n^12 + (48277/14370048000)*n^11 - (293/3483648)*n^10 + (787333/365783040)*n^9 - (24368131/609638400)*n^8 + (200509627/326592000)*n^7 - (316559651/43545600)*n^6 + (9499836221/143700480)*n^5 - (53265620347/119750400)*n^4 + (19358243050561/9081072000)*n^3 - (1030835612797/151351200)*n^2 + (36972827/2860)*n - 10961 for n>4
%e Some solutions for n=9
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0
%e ..0..1..1..1....0..0..1..1....0..0..0..1....0..1..0..1....0..0..0..0
%e ..0..1..1..1....0..1..1..1....0..1..1..1....0..1..0..1....0..0..1..1
%e ..1..0..0..1....1..0..0..1....1..0..0..0....1..0..0..0....0..0..1..1
%e ..1..0..1..0....1..1..0..1....1..0..1..0....1..0..0..1....1..1..0..1
%e ..1..0..1..0....1..1..0..1....1..0..1..0....1..0..0..1....1..1..0..1
%e ..1..0..1..1....1..1..1..1....1..1..0..1....1..0..1..1....1..1..0..1
%e ..1..1..1..1....1..1..1..1....1..1..0..1....1..1..1..1....1..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 30 2011