A298362 - OEIS

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

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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