This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A228107 Triangle read by rows: T(n,k) (1<=k<=n) = number of runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of an n X k rectangle into integer sided squares, considering only the list of parts, where partition sorting order is ascending with larger squares taking higher precedence. 2
 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 4, 1, 1, 3, 4, 5, 8, 1, 1, 3, 5, 6, 10, 12, 1, 1, 3, 6, 8, 13, 17, 22 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The triangle begins: \ k  1  2  3  4  5  6  7  8 ... n 1    1 2    1  1 3    1  1  2 4    1  1  2  3 5    1  1  2  3  4 6    1  1  3  4  5  8 7    1  1  3  5  6 10 12 8    1  1  3  6  8 13 17 22 LINKS Christopher Hunt Gribble, C++ program EXAMPLE T(5,4) = 3 because there are 3 runs of strictly increasing numbers of 2 X 2 squares in the list of partitions of a 5 X 4 rectangle into integer sided squares.  The list of partitions is: .            Square side Run         1   2   3   4 . 1        20   0   0   0 .          16   1   0   0 .          12   2   0   0 .           8   3   0   0 .           4   4   0   0 . 2        11   0   1   0 .           7   1   1   0 .           3   2   1   0 . 3         4   0   0   1 CROSSREFS Diagonal is A226947. Cf. A228106 Sequence in context: A176484 A144328 A128227 * A140207 A104763 A027751 Adjacent sequences:  A228104 A228105 A228106 * A228108 A228109 A228110 KEYWORD nonn,tabl AUTHOR Christopher Hunt Gribble, Aug 10 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 08:50 EST 2018. Contains 318148 sequences. (Running on oeis4.)