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.

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

Table of n, a(n) for n=1..43.

Roberto Tauraso, Problem 12005, Proposed solution.

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

See Vladimirov link.

Crossrefs

Cf. A000295, A285357, A285361, A336732, A336734.

Sequence in context: A342643 A109088 A060923 * A143952 A097877 A225770

Adjacent sequences: A298359 A298360 A298361 * A298363 A298364 A298365

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