cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A172477 The number of ways to dissect an n X n square into polyominoes of size n.

Original entry on oeis.org

1, 2, 10, 117, 4006, 451206, 158753814, 187497290034, 706152947468301
Offset: 1

Views

Author

Johan de Ruiter, Feb 04 2010

Keywords

Examples

			A 2 X 2 square can be covered by two dominoes by either positioning them vertically or horizontally.
		

Crossrefs

Intersects with A167251, A167254, A167255, A167258.
Diagonal of A348452.

Formula

a(3) = A167243(3). a(4) = A167248(4). a(5) = A167251(5). a(6) = A167254(6). a(7) = A167255(7). a(8) = A167258(8). - R. J. Mathar, Oct 13 2024

Extensions

a(9) from Bob Harris (me13013(AT)gmail.com), Mar 13 2010

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

Original entry on oeis.org

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
Offset: 0

Views

Author

R. H. Hardin, Oct 31 2009

Keywords

Examples

			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
		

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.

Crossrefs

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

Extensions

a(0) = 1 prepended by Don Knuth, May 11 2016
Terms a(21) and beyond from Roberto Tauraso, Oct 11 2016
Showing 1-2 of 2 results.