A275662 Triangle read by rows: T(n,k) = number of convex domino towers with n dominoes having widest row with k dominoes.

1, 3, 1, 7, 6, 1, 15, 18, 7, 1, 31, 48, 17, 9, 1, 63, 109, 49, 20, 11, 1, 127, 240, 115, 52, 24, 13, 1, 255, 498, 258, 122, 61, 28, 15, 1, 511, 1026, 551, 261, 136, 71, 32, 17, 1, 1023, 2065, 1163, 531, 298, 157, 81, 36, 19, 1

Offset: 1

Author

Tricia Muldoon Brown, Aug 04 2016

Keywords

• nonn
• tabl
• more

Comments

A domino tower is built by placing dominoes horizontally on a convex horizontal base. A domino tower is convex if all its columns and rows are convex.

Examples

			Triangle begins:
1;
3, 1;
7, 6, 1;
15, 18, 7, 1;
...
If n = 3 and k = 2, the widest row of the domino tower has two dominoes. Thus the third domino may be found supporting the row of two dominoes in one way or being supported by the row of two dominoes in 5 ways, so T(3,2) = 6.
		

Links

• T. M. Brown, Convex domino towers, arXiv:1608.01562 [math.CO] (2016).

Crossrefs

Column 1: A000225, n>=1.

Cf. A117468, A275204, A275599.

Formula

G.f.: (2*A_k(x)+B_k(x))*(C_{k-1}(x)+1) where A_k(x) is the generating function on right-skewed domino towers with a base of k dominoes from the sequence A275599, B_k(x) is the generating function on domino stacks with a base of k dominoes associated with the sequence A275204, and C_k(x) is the generating function on flat partitions whose largest part is k-1 given by the sequence A117468.