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%I #25 Dec 06 2022 17:53:44
%S 1,3,19,85,355,1435,5717,22645,89521,353735,1397863,5525341,21846421,
%T 86403027,341822335,1352660761,5354124895,21197945407,83945924393,
%U 332507403625,1317329758675,5220055148883,20688989887169,82013159349085,325165555406795,1289434099001055,5114044079094817,20286061330030705,80481556028898031
%N Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions.
%D D. E. Knuth (Proposer) and Editors (Solver), Balanced tilings of a rectangle with three rows, Problem 11929, Amer. Math. Monthly, 125 (2018), 566-568.
%H Manuel Kauers, Christoph Koutschan, and George Spahn, <a href="https://arxiv.org/abs/2209.01787">A348456(4) = 7157114189</a>, arXiv:2209.01787 [math.CO], 2022.
%H Manuel Kauers, Christoph Koutschan, and George Spahn, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Kauers/kauers6.html">How Does the Gerrymander Sequence Continue?</a>, J. Int. Seq., Vol. 25 (2022), Article 22.9.7.
%F The solution to the Knuth problem gives an explicit g.f. and an explicit formula for a(n) in terms of Fibonacci numbers. - _N. J. A. Sloane_, May 25 2018
%e Some solutions for n=4
%e ...1.1.1...1.1.1...1.1.2...1.1.2...1.1.2...1.1.1...1.1.1...1.1.1...1.1.1
%e ...1.1.1...1.1.2...1.2.2...1.1.2...1.2.2...2.2.1...1.1.1...2.1.1...1.1.1
%e ...2.2.1...1.2.2...1.1.2...1.2.2...1.2.2...2.2.1...2.1.1...2.2.1...2.1.1
%e ...2.1.1...1.2.2...1.2.2...1.2.2...1.1.2...2.2.1...2.2.1...2.1.1...2.2.1
%e ...2.2.1...1.2.2...1.1.2...1.2.2...1.1.2...2.1.1...2.2.1...2.2.1...2.2.1
%e ...2.2.1...1.1.2...1.1.2...1.2.2...1.1.2...2.1.1...2.1.1...2.1.1...2.2.1
%e ...2.2.1...1.2.2...1.2.2...1.1.2...1.1.2...2.1.1...2.2.2...2.1.2...2.2.1
%e ...2.2.2...1.2.2...1.2.2...1.1.2...2.2.2...2.2.2...2.2.2...2.2.2...2.2.2
%Y Cf. A000045, A167243.
%K nonn
%O 0,2
%A _R. H. Hardin_, Oct 31 2009
%E a(0) = 1 prepended by _Don Knuth_, May 11 2016
%E Terms a(21) and beyond from _Roberto Tauraso_, Oct 11 2016
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