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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.

%I A298362 #43 Jun 07 2024 10:57:27
%S A298362 1,1,4,1,11,64,1,26,282,2072,1,57,1071,12279,106738,1,120,3729,63858,
%T A298362 781458,7743880,1,247,12310,305464,5111986,66679398,735490024,1,502,
%U A298362 39296,1382648,30980370,521083252,7216122740,87138728592,1,1013,122773,6029325,178047831,3802292847,65106398091
%N 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.
%C A298362 See A285357.
%C A298362 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
%H A298362 Roberto Tauraso, <a href="http://www.mat.uniroma2.it/~tauraso/AMM/AMM12005.pdf">Problem 12005, Proposed solution</a>.
%H A298362 Konstantin Vladimirov, <a href="https://github.com/tilir/generators">Generating things</a>, Program naivepavings.cc to enumerate all tight pavings.
%e A298362 The triangle starts:
%e A298362 ================================================================================
%e A298362 m \ n| 1    2      3        4         5           6           7           8    9
%e A298362 -----|--------------------------------------------------------------------------
%e A298362 .  1 | 1
%e A298362 .  2 | 1    4
%e A298362 .  3 | 1   11     64
%e A298362 .  4 | 1   26    282     2072
%e A298362 .  5 | 1   57   1071    12279    106738
%e A298362 .  6 | 1  120   3729    63858    781458     7743880
%e A298362 .  7 | 1  247  12310   305464   5111986    66679398   735490024
%e A298362 .  8 | 1  502  39296  1382648  30980370   521083252  7216122740 87138728592
%e A298362 .  9 | 1 1013 122773  6029325 178047831  3802292847 65106398091      ?         ?
%e A298362 . 10 | 1 2036 378279 25628762 985621119 26409556208         ...
%o A298362 (C++) // See Vladimirov link.
%Y A298362 Cf. A000295, A285357, A285361, A336732, A336734.
%K A298362 nonn,tabl
%O A298362 1,3
%A A298362 _Hugo Pfoertner_, Jan 17 2018
%E A298362 Added a number of values in the example table, _Denis Roegel_, Feb 24 2018
%E A298362 Extended using data from _Denis Roegel_ by _Hugo Pfoertner_, Mar 12 2018