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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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.

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      ?          ...

PROG

See Vladimirov link.

CROSSREFS

Cf. A000295, A285357, A285361.

Sequence in context: A181690 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

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)