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 A167242 Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions. 2
 1, 3, 19, 85, 355, 1435, 5717, 22645, 89521, 353735, 1397863, 5525341, 21846421, 86403027, 341822335, 1352660761, 5354124895, 21197945407, 83945924393, 332507403625, 1317329758675, 5220055148883, 20688989887169, 82013159349085, 325165555406795, 1289434099001055, 5114044079094817, 20286061330030705, 80481556028898031 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES D. E. Knuth (Proposer) and Editors (Solver), Balanced tilings of a rectangle with three rows, Problem 11929, Amer. Math. Monthly, 125 (2018), 566-568. LINKS Table of n, a(n) for n=0..28. Manuel Kauers, Christoph Koutschan, and George Spahn, A348456(4) = 7157114189, arXiv:2209.01787 [math.CO], 2022. Manuel Kauers, Christoph Koutschan, and George Spahn, How Does the Gerrymander Sequence Continue?, J. Int. Seq., Vol. 25 (2022), Article 22.9.7. FORMULA 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 EXAMPLE Some solutions for n=4 ...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 ...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 ...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 ...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 ...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 ...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 ...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 ...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 CROSSREFS Cf. A000045, A167243. Sequence in context: A293561 A240286 A163431 * A089621 A204256 A015528 Adjacent sequences: A167239 A167240 A167241 * A167243 A167244 A167245 KEYWORD nonn AUTHOR R. H. Hardin, Oct 31 2009 EXTENSIONS a(0) = 1 prepended by Don Knuth, May 11 2016 Terms a(21) and beyond from Roberto Tauraso, Oct 11 2016 STATUS approved

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Last modified December 8 23:37 EST 2023. Contains 367681 sequences. (Running on oeis4.)