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Revision History for A000285 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.
(history; published version)
#186 by N. J. A. Sloane at Fri Sep 13 08:12:53 EDT 2024
STATUS

proposed

approved

#185 by Greg Dresden at Sat Sep 07 10:50:39 EDT 2024
STATUS

editing

proposed

#184 by Greg Dresden at Sat Sep 07 10:50:00 EDT 2024
COMMENTS

For n>2, a(n) + (-1)^ceiling(n/2) is the number of ways to tile this strip of length n-1, with a central staircase, using unit squares and dominoes:

STATUS

proposed

editing

Discussion
Sat Sep 07
10:50
Greg Dresden: Sorry, it's unit squares! I've made an edit to clear up the ambiguity.
#183 by Michel Marcus at Sat Sep 07 10:22:04 EDT 2024
STATUS

editing

proposed

Discussion
Sat Sep 07
10:35
Andrew Howroyd: Are the squares always unit squares, or is a 2 X 2 square also allowed? (in the central staircase)
#182 by Michel Marcus at Sat Sep 07 10:22:02 EDT 2024
COMMENTS

For n>2, a(n) + (-1)^Ceilingceiling(n/2) is the number of ways to tile this strip of length n-1, with a central staircase, using squares and dominoes:

STATUS

proposed

editing

#181 by Greg Dresden at Sat Sep 07 09:22:14 EDT 2024
STATUS

editing

proposed

#180 by Greg Dresden at Sat Sep 07 09:21:27 EDT 2024
COMMENTS

For n>2, a(n) + (-1)^Ceiling(n/2) is the number of ways to tile this strip of length n-1, with a central staircase, using squares and dominoes: _

_

_______|_|_|_________

_______|_|_|_________|_|_|_|_|_|_|_|_|_|_|_|. - Greg Dresden, and Runhe Zhang, Sep 07 2024

#179 by Greg Dresden at Sat Sep 07 09:20:26 EDT 2024
COMMENTS

For n>2, a(n) + (-1)^Ceiling(n/2) is the number of ways to tile this strip of length n-1, with a central staircase, using squares and dominoes: _

_|_|

_______|_|_|_________|_|_|_|_|_|_|_|_|_|_|_|. - Greg Dresden, Sep 07 2024

STATUS

approved

editing

#178 by Michael De Vlieger at Fri Mar 29 11:44:16 EDT 2024
STATUS

reviewed

approved

#177 by Michel Marcus at Fri Mar 29 11:39:44 EDT 2024
STATUS

proposed

reviewed