A298432 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).

1, 2, 6, 24, 118, 680, 4456, 32512, 260080, 2254464, 20982768, 208142912, 2187336048, 24229170560

Offset

1,2

Links

Table of n, a(n) for n=1..14.

D. E. Knuth (Proposer), Tight m-by-n pavings; Problem 12005, Amer. Math. Monthly 124 (No. 8, Oct. 2017), page 755.

D. E. Knuth, A conjecture that had to be true, Stanford Lecture: Don Knuth's Christmas Tree Lecture 2017.

Example

These are the row sums of A285357 if A285357 is written as a triangle:
1;
1,   1;
1,   4,     1;
1,  11,    11,     1;
1,  26,    64,    26,      1;
1,  57,   282,   282,     57,     1;
1, 120,  1071,  2072,   1071,   120,     1;
1, 247,  3729, 12279,  12279,  3729,   247,   1;
1, 502, 12310, 63858, 106738, 63858, 12310, 502, 1;

Crossrefs

Cf. A000295, A285357, A285361, A298362.

Sequence in context: A263777 A088713 A193938 * A336072 A328501 A328442

Adjacent sequences: A298429 A298430 A298431 * A298433 A298434 A298435

Keyword

nonn,more

Author

Peter Luschny, Jan 19 2018

Extensions

a(11) from Hugo Pfoertner, Jan 19 2018

a(12)-a(14) from Denis Roegel, Feb 24 2018

Status

approved