A166826 - OEIS

%I #7 Mar 26 2018 09:54:31

%S 0,4,49,219,666,1636,3499,6783,12212,20748,33637,52459,79182,116220,

%T 166495,233503,321384,434996,579993,762907,991234,1273524,1619475,

%U 2040031,2547484,3155580,3879629,4736619,5745334,6926476,8302791,9899199

%N Number of n X 2 1..4 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.

%H R. H. Hardin, <a href="/A166826/b166826.txt">Table of n, a(n) for n=1..44</a>

%F Empirical: a(n) = (n^6 + 18*n^5 + 100*n^4 - 731*n^2 + 792*n - 180)/180.

%F Conjectures from _Colin Barker_, Mar 26 2018: (Start)

%F G.f.: x^2*(4 + 21*x - 40*x^2 + 22*x^3 - 2*x^4 - x^5) / (1 - x)^7.

%F 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>7.

%F (End)

%e All solutions for n=3:

%e ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...2.1...2.1...2.1...2.1

%e ...2.1...2.1...2.2...3.1...3.2...3.2...3.2...3.3...4.2...2.1...2.1...2.2...2.2

%e ...3.4...4.3...4.3...4.2...3.4...4.2...4.4...4.2...4.3...3.4...4.3...3.4...4.3

%e ------

%e ...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1

%e ...2.3...2.3...2.3...2.4...2.4...3.1...3.1...3.1...3.3...3.3...3.3...3.4...3.4

%e ...2.4...4.3...4.4...3.3...3.4...3.4...4.1...4.4...3.4...4.3...4.4...3.4...4.4

%e ------

%e ...2.1...2.1...2.1...2.2...2.2...2.2...2.2...2.2...2.2...3.1...3.1...3.1...3.1

%e ...4.1...4.3...4.3...3.1...3.1...3.1...3.2...3.3...4.1...3.1...3.2...3.2...3.2

%e ...4.3...4.3...4.4...3.4...4.1...4.4...4.1...4.1...4.3...4.2...3.4...4.2...4.4

%e ------

%e ...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.3...4.1

%e ...3.3...4.1...4.2...4.2...3.2...3.3...4.1...4.1...4.1...4.2

%e ...4.2...4.2...4.2...4.4...4.1...4.1...4.1...4.4...4.2...4.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009