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A167242 Number of ways to partition a 2*n X 3 grid into 2 connected equal-area regions. 1
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.

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 4 22:42 EST 2021. Contains 349526 sequences. (Running on oeis4.)