A298432 - OEIS

%I #13 Feb 24 2018 10:14:07

%S 1,2,6,24,118,680,4456,32512,260080,2254464,20982768,208142912,

%T 2187336048,24229170560

%N a(n) = Sum_{k=0..n-1} T(n-k, k+1) where T(n, k) is the number of tight n X k pavings (defined in A285357).

%H D. E. Knuth (Proposer), <a href="http://dx.doi.org/10.4169/amer.math.monthly.124.8.754">Tight m-by-n pavings; Problem 12005</a>, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755.

%H D. E. Knuth, <a href="https://www.youtube.com/watch?v=BxQw4CdxLr8">A conjecture that had to be true</a>, Stanford Lecture: Don Knuth's Christmas Tree Lecture 2017.

%e These are the row sums of A285357 if A285357 is written as a triangle:

%e 1;

%e 1,   1;

%e 1,   4,     1;

%e 1,  11,    11,     1;

%e 1,  26,    64,    26,      1;

%e 1,  57,   282,   282,     57,     1;

%e 1, 120,  1071,  2072,   1071,   120,     1;

%e 1, 247,  3729, 12279,  12279,  3729,   247,   1;

%e 1, 502, 12310, 63858, 106738, 63858, 12310, 502, 1;

%Y Cf. A000295, A285357, A285361, A298362.

%K nonn,more

%O 1,2

%A _Peter Luschny_, Jan 19 2018

%E a(11) from _Hugo Pfoertner_, Jan 19 2018

%E a(12)-a(14) from _Denis Roegel_, Feb 24 2018