A184547 - OEIS

%I #9 Apr 14 2018 07:33:49

%S 682,2000,4837,10909,23648,49489,99872,194245,364432,660821,1160932,

%T 1981045,3291704,5338066,8466235,13156911,20067894,30087214,44398911,

%U 64563765,92617576,131189919,183646650,254259817,348409036,472818827

%N Number of (n+2) X 10 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%C Column 8 of A184548.

%H R. H. Hardin, <a href="/A184547/b184547.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/3628800)*n^10 + (1/48384)*n^9 + (83/120960)*n^8 + (107/8064)*n^7 + (28573/172800)*n^6 + (5323/3840)*n^5 + (1434973/181440)*n^4 + (366371/12096)*n^3 + (2399357/12600)*n^2 + (151541/420)*n + 91.

%F Conjectures from _Colin Barker_, Apr 14 2018: (Start)

%F G.f.: x*(682 - 5502*x + 20347*x^2 - 44828*x^3 + 64744*x^4 - 63833*x^5 + 43442*x^6 - 20156*x^7 + 6118*x^8 - 1104*x^9 + 91*x^10) / (1 - x)^11.

%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

%F (End)

%e Some solutions for 4 X 10:

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

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

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

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

%Y Cf. A184548.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2011