cp's OEIS Frontend

A167242 Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions.

%I A167242 #25 Dec 06 2022 17:53:44
%S A167242 1,3,19,85,355,1435,5717,22645,89521,353735,1397863,5525341,21846421,
%T A167242 86403027,341822335,1352660761,5354124895,21197945407,83945924393,
%U A167242 332507403625,1317329758675,5220055148883,20688989887169,82013159349085,325165555406795,1289434099001055,5114044079094817,20286061330030705,80481556028898031
%N A167242 Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions.
%D A167242 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 A167242 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 A167242 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 A167242 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 A167242 Some solutions for n=4
%e A167242 ...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 A167242 ...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 A167242 ...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 A167242 ...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 A167242 ...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 A167242 ...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 A167242 ...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 A167242 ...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 A167242 Cf. A000045, A167243.
%K A167242 nonn
%O A167242 0,2
%A A167242 _R. H. Hardin_, Oct 31 2009
%E A167242 a(0) = 1 prepended by _Don Knuth_, May 11 2016
%E A167242 Terms a(21) and beyond from _Roberto Tauraso_, Oct 11 2016