login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A223395 4 X 4 square grid graph coloring a rectangular array: number of n X 1 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph. 1
16, 48, 152, 488, 1576, 5096, 16488, 53352, 172648, 558696, 1807976, 5850728, 18933352, 61269608, 198272616, 641623656, 2076337768, 6719170152, 21743691368, 70364063336, 227702892136, 736862037608, 2384535643752, 7716519437928 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 1 of A223402.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 4*a(n-3).
Conjectures from Colin Barker, Aug 20 2018: (Start)
G.f.: 8*x*(2 - 3*x^2) / ((1 - x)*(1 - 2*x - 4*x^2)).
a(n) = (8 + (11-5*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(11+5*sqrt(5))) / 5.
(End)
EXAMPLE
Some solutions for n=3:
.12....9....5....0...10....2....5....0....7....1...10....6...12...11...15....2
..8...13....6....1....9....3....6....4....3....0....9...10...13...10...11....1
.12...12....2....2....8....2....5....5....2....1...10...11....9...11...10....0
Vertex neighbors:
0 -> 1 4
1 -> 0 2 5
2 -> 1 3 6
3 -> 2 7
4 -> 0 5 8
5 -> 4 1 6 9
6 -> 5 2 7 10
7 -> 6 3 11
8 -> 4 9 12
9 -> 8 5 10 13
10 -> 9 6 11 14
11 -> 10 7 15
12 -> 8 13
13 -> 12 9 14
14 -> 13 10 15
15 -> 14 11
CROSSREFS
Cf. A223402.
Sequence in context: A211598 A235541 A109098 * A202329 A223599 A223692
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 19 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 12:17 EST 2024. Contains 370235 sequences. (Running on oeis4.)