A166829 - OEIS

%I #11 May 26 2016 02:26:13

%S 0,0,0,714,10101,67447,306569,1094959,3307802,8826810,21396106,

%T 48023760,101191247,202227753,386326083

%N Number of nX2 1..7 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nonincreasing order.

%F From _G. C. Greubel_, May 25 2016: (Start)

%F Empirical: a(n) = (32/(12)!)*(n-1)*(n-2)*(n-3)*(n^9 + 78*n^8 + 3141*n^7 + 75084*n^6 + 994614*n^5 + 5642142*n^4 - 2217436*n^3 - 75779064*n^2 + 77727420*n - 2494800).

%F Empirical G.f.: (1 - 13*x + 78*x^2 - 286*x^3 + 1429*x^4 - 468*x^5 - 6458*x^6 + 11716*x^7 - 6661*x^8 - 1543*x^9 + 3580*x^10 - 1582*x^11 + 239*x^12)/(1 - x)^13 - 1.

%F Empirical E.g.f.: (32/(12)!)*(14968800 - 14968800*x + 7484400*x^2 - 2494800*x^3 + 445945500*x^4 + 814552200*x^5 + 364906080*x^6 + 64062900*x^7 + 5660820*x^8 + 283305*x^9 + 8349*x^10 + 138*x^11 + x^12)*exp(x) - 1. (End)

%e Some solutions for n=4

%e ...2.1...3.2...2.1...4.2...3.2...4.3...2.1...2.1...2.1...3.1...2.1...4.1...3.2

%e ...2.3...4.1...3.6...6.3...4.1...5.1...4.7...3.6...3.7...4.2...2.3...4.3...4.2

%e ...4.7...5.5...5.4...6.5...6.1...6.6...6.3...4.4...4.6...5.6...4.5...6.5...6.5

%e ...5.6...7.6...7.7...7.1...7.5...7.2...6.5...5.7...5.5...5.7...7.6...7.2...7.1

%e ------

%e ...4.3...3.2...2.1...3.1...3.1...4.1...3.1...3.1...4.3...2.1...2.1...3.1...2.1

%e ...6.1...3.7...2.6...4.1...5.2...4.2...4.2...3.2...5.2...3.5...2.7...5.4...4.6

%e ...7.2...4.1...4.7...5.6...6.4...5.3...5.5...4.7...6.6...3.6...3.4...6.2...5.3

%e ...7.5...5.6...5.3...7.2...7.4...7.6...7.6...5.6...7.1...7.4...6.5...7.2...7.3

%K nonn

%O 1,4

%A _R. H. Hardin_, Oct 21 2009