A166808 - OEIS

%I #30 May 25 2016 22:04:11

%S 4,19,54,124,250,460,790,1285,2000,3001,4366,6186,8566,11626,15502,

%T 20347,26332,33647,42502,53128,65778,80728,98278,118753,142504,169909,

%U 201374,237334,278254,324630,376990,435895,501940,575755,658006,749396,850666,962596

%N Number of n X 5 1..2 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 nondecreasing order.

%H G. C. Greubel, <a href="/A166808/b166808.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = binomial(n+5,5) - 2. - _Jeffrey Shallit_, May 30 2012

%F From _G. C. Greubel_, May 24 2016: (Start)

%F G.f.: 1/(1-x)^6 - (1+x)/(1-x).

%F E.g.f.: (1/5!)*(x^5 + 25*x^4 + 200*x^3 + 600*x^2 + 600*x -120)*exp(x) +1. (End)

%e Some solutions for n=4

%e ...1.1.1.1.1...1.1.1.1.1...1.1.1.1.1...1.1.1.1.1...1.1.1.1.2...1.1.1.1.2

%e ...1.1.1.1.1...1.1.1.1.1...1.1.1.1.2...1.1.1.2.2...1.1.1.2.2...1.1.1.1.2

%e ...1.1.2.2.2...1.1.1.2.2...1.1.1.2.2...2.2.2.2.2...1.1.2.2.2...1.1.1.2.2

%e ...1.1.2.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...1.1.2.2.2...1.1.1.2.2

%e ------

%e ...1.1.1.1.1...1.1.1.1.2...1.1.1.2.2...1.1.1.2.2...1.2.2.2.2...1.1.1.2.2

%e ...1.1.1.2.2...1.1.1.1.2...1.1.2.2.2...2.2.2.2.2...1.2.2.2.2...1.1.1.2.2

%e ...1.1.1.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...2.2.2.2.2...2.2.2.2.2

%e ...2.2.2.2.2...2.2.2.2.2...1.1.2.2.2...2.2.2.2.2...2.2.2.2.2...2.2.2.2.2

%t Table[Binomial[n+5,5] -2, {n, 1, 100}] (* _G. C. Greubel_, May 24 2016 *)

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 21 2009