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

1,2

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.

Links

Table of n, a(n) for n=1..55.

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

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.

Example

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.

Crossrefs

Column 1: A000225, n>=1.

Cf. A117468, A275204, A275599.

Sequence in context: A166519 A213043 A319740 * A110441 A111806 A321163

Adjacent sequences: A275659 A275660 A275661 * A275663 A275664 A275665

Keyword

nonn,tabl,more

Author

Tricia Muldoon Brown, Aug 04 2016

Status

approved