

A167242


Number of ways to partition a 2*n X 3 grid into 2 connected equalarea 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), 566568.


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



