A166842 - OEIS

%I #15 Oct 09 2023 17:18:29

%S 1,14,78,284,807,1946,4172,8184,14973,25894,42746,67860,104195,155442,

%T 226136,321776,448953,615486,830566,1104908,1450911

%N Number of n X 3 1..3 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 decreasing order.

%F Empirical: a(n) = (1/90)*n*(n^5 + 9*n^4 + 40*n^3 + 30*n^2 + 4*n + 6).

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

%F Empirical G.f.: x*(1 + 7*x + x^2 - 3*x^3 + 2*x^4)/(1 - x)^7.

%F Empirical E.g.f.: (1/90)*x*(90 + 540*x + 585*x^2 + 195*x^3 + 24*x^4 + x^5)*exp(x). (End)

%e Some solutions for n=4:

%e ...3.1.1...3.2.1...3.1.1...2.1.1...2.1.1...2.1.1...2.2.1...3.1.1...1.1.1

%e ...3.3.1...3.2.2...3.2.1...2.2.1...2.2.1...3.3.1...3.2.2...3.1.1...3.2.1

%e ...3.3.1...3.2.2...3.3.1...3.1.1...3.2.1...3.3.1...3.3.2...3.2.2...3.3.3

%e ...3.3.2...3.3.2...3.3.3...3.3.3...3.3.1...3.3.1...3.3.3...3.3.2...3.3.3

%e ------

%e ...2.2.1...1.1.1...1.1.1...1.1.1...3.1.1...3.2.2...2.2.1...2.1.1...1.1.1

%e ...3.2.2...1.1.1...3.2.1...3.2.1...3.1.1...3.2.2...3.2.1...2.1.1...2.1.1

%e ...3.3.3...3.2.1...3.2.1...3.2.3...3.2.1...3.2.2...3.3.1...2.2.1...3.3.1

%e ...3.3.3...3.3.1...3.2.2...3.3.3...3.2.2...3.3.1...3.3.1...3.1.1...3.3.1

%K nonn,more

%O 1,2

%A _R. H. Hardin_, Oct 21 2009