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
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).
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.
Comments