cp's OEIS Frontend

A220037 Number of 7 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 7 X n array.

%I A220037 #7 Jul 30 2018 08:13:28
%S A220037 8,14,36,119,297,626,1165,1963,3088,4630,6711,9492,13175,18010,24304,
%T A220037 32431,42843,56082,72793,93738,119811,152054,191674,240061,298807,
%U A220037 369726,454875,556576,677439,820386,988676,1185931,1416163,1683802,1993725
%N A220037 Number of 7 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 7 X n array.
%C A220037 Row 7 of A220032.
%H A220037 R. H. Hardin, <a href="/A220037/b220037.txt">Table of n, a(n) for n = 1..53</a>
%F A220037 Empirical: a(n) = (1/720)*n^6 - (7/240)*n^5 + (107/144)*n^4 - (209/48)*n^3 + (1609/45)*n^2 + (1913/60)*n - 813 for n>9.
%F A220037 Conjectures from _Colin Barker_, Jul 30 2018: (Start)
%F A220037 G.f.: x*(8 - 42*x + 106*x^2 - 119*x^3 + 10*x^4 + 108*x^5 - 123*x^6 + 58*x^7 + 36*x^8 - 68*x^9 + 33*x^10 - 10*x^11 - 2*x^12 + 10*x^13 - 3*x^14 - x^15) / (1 - x)^7.
%F A220037 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>16.
%F A220037 (End)
%e A220037 Some solutions for n=3:
%e A220037 ..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A220037 ..0..0..0....1..1..1....1..0..0....1..0..0....0..0..0....1..0..0....0..0..0
%e A220037 ..1..0..0....1..1..1....1..0..0....1..1..1....0..0..0....1..0..0....0..0..0
%e A220037 ..1..0..0....1..1..1....1..0..0....1..1..1....0..0..0....1..0..0....1..0..0
%e A220037 ..1..0..0....1..1..1....1..1..1....1..1..1....0..0..0....1..0..0....1..0..0
%e A220037 ..1..1..1....1..1..1....1..1..1....1..1..1....0..0..0....1..1..1....1..0..0
%e A220037 ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....1..1..1....1..1..1
%Y A220037 Cf. A220032.
%K A220037 nonn
%O A220037 1,1
%A A220037 _R. H. Hardin_, Dec 03 2012