|
%I #8 Jul 25 2018 08:37:31
%S 4,9,42,149,423,1092,2623,5937,12729,26009,50896,95774,173920,305737,
%T 521743,866485,1403565,2221983,3444020,5234902,7814504,11471371,
%U 16579351,23617153,33191161,46061853,63174192,85692374,115039336,152941445
%N Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.
%C Column 4 of A219291.
%H R. H. Hardin, <a href="/A219287/b219287.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/2240)*n^8 - (1/90)*n^7 + (17/96)*n^6 - (373/360)*n^5 - (4459/960)*n^4 + (49529/360)*n^3 - (348947/336)*n^2 + (55477/15)*n - 5259 for n>6.
%F Conjectures from _Colin Barker_, Jul 25 2018: (Start)
%F G.f.: x*(4 - 27*x + 105*x^2 - 241*x^3 + 342*x^4 - 249*x^5 + x^6 + 204*x^7 - 240*x^8 + 223*x^9 - 206*x^10 + 161*x^11 - 76*x^12 + 22*x^13 - 5*x^14) / (1 - x)^9.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>15.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1..1....0..0..0..0....0..0..0..1....0..0..0..0....0..0..0..0
%e ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0
%e ..1..0..0..0....1..1..1..1....1..0..0..1....0..0..0..0....0..0..0..1
%Y Cf. A219291.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 17 2012
| 