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A298362
Number of tight m X n pavings as defined in Knuth's A285357 written as triangle T(m,n), m >= 1, 1 <= n <= m.
4
1, 1, 4, 1, 11, 64, 1, 26, 282, 2072, 1, 57, 1071, 12279, 106738, 1, 120, 3729, 63858, 781458, 7743880, 1, 247, 12310, 305464, 5111986, 66679398, 735490024, 1, 502, 39296, 1382648, 30980370, 521083252, 7216122740, 87138728592, 1, 1013, 122773, 6029325, 178047831, 3802292847, 65106398091
OFFSET
1,3
COMMENTS
See A285357.
For m < n, one has A285357(m,n) = T(n,m). Thus, row and column n of A285357 start with the n terms of row n, then go on downwards in column n: e.g., the full row/column 2 is (1, 4, 11, 26, ...) = A000295 (without initial 0); row/column 3 is (1, 11, 64, 282, 1071, ...) = A285361. - M. F. Hasler, Jan 20 2018
LINKS
Konstantin Vladimirov, Generating things, Program naivepavings.cc to enumerate all tight pavings.
EXAMPLE
The triangle starts:
================================================================================
m \ n| 1 2 3 4 5 6 7 8 9
-----|--------------------------------------------------------------------------
. 1 | 1
. 2 | 1 4
. 3 | 1 11 64
. 4 | 1 26 282 2072
. 5 | 1 57 1071 12279 106738
. 6 | 1 120 3729 63858 781458 7743880
. 7 | 1 247 12310 305464 5111986 66679398 735490024
. 8 | 1 502 39296 1382648 30980370 521083252 7216122740 87138728592
. 9 | 1 1013 122773 6029325 178047831 3802292847 65106398091 ? ?
. 10 | 1 2036 378279 25628762 985621119 26409556208 ...
PROG
(C++) // See Vladimirov link.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugo Pfoertner, Jan 17 2018
EXTENSIONS
Added a number of values in the example table, Denis Roegel, Feb 24 2018
Extended using data from Denis Roegel by Hugo Pfoertner, Mar 12 2018
STATUS
approved