A201373 - OEIS

%I #8 May 22 2018 20:27:33

%S 2,7,32,157,786,3739,15574,55410,170616,465037,1145954,2597729,

%T 5492076,10947133,20749996,37660122,65814022,111254955,182614908,

%U 291980013,455974718,697104503,1045401722,1540424266,2233662188,3191413217

%N Number of n X 6 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

%C Column 6 of A201375.

%H R. H. Hardin, <a href="/A201373/b201373.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/453600)*n^10 + (1/2160)*n^9 + (227/60480)*n^8 - (73/1260)*n^7 + (1319/10800)*n^6 + (757/720)*n^5 - (881131/181440)*n^4 + (2207/540)*n^3 + (396407/25200)*n^2 - (6737/210)*n + 18.

%F Conjectures from _Colin Barker_, May 22 2018: (Start)

%F G.f.: x*(2 - 15*x + 65*x^2 - 140*x^3 + 324*x^4 - 166*x^5 + 20*x^6 - 349*x^7 + 391*x^8 - 142*x^9 + 18*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 n=5:

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

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

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

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

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

%Y Cf. A201375.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2011