|
%I #9 Aug 27 2018 08:14:37
%S 128,2187,9688,25047,52581,101412,186348,329167,561329,927323,1488515,
%T 2327716,3554534,5311574,7781550,11195373,15841279,22075061,30331469,
%U 41136842,55123036,73042712,95786048,124398939,160102749,204315679
%N Number of 7 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
%C Row 7 of A224133.
%H R. H. Hardin, <a href="/A224138/b224138.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (112/45)*n^5 + (461/24)*n^4 + (19267/180)*n^3 + (50171/120)*n^2 + (463243/420)*n - 511 for n>5.
%F Conjectures from _Colin Barker_, Aug 27 2018: (Start)
%F G.f.: x*(128 + 1163*x - 4224*x^2 + 1611*x^3 + 9957*x^4 - 14526*x^5 + 3960*x^6 + 4357*x^7 - 1401*x^8 - 1818*x^9 + 659*x^10 + 353*x^11 - 155*x^12) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1
%e ..0..1..1....0..0..1....1..1..1....1..1..1....1..1..1....0..0..0....0..0..1
%e ..0..0..1....0..0..1....1..1..1....1..1..1....0..0..1....0..1..1....0..1..1
%e ..0..0..0....0..0..1....0..0..0....0..1..1....0..0..0....1..1..1....0..0..0
%e ..0..1..1....0..0..1....0..1..1....0..0..0....0..0..0....0..0..1....0..1..1
%e ..0..0..0....0..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..0..0
%e ..0..0..1....0..0..1....0..0..0....0..0..0....1..1..1....0..0..0....0..0..0
%Y Cf. A224133.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 31 2013
| 