cp's OEIS Frontend

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

%I A275662 #17 Aug 31 2016 17:56:57
%S A275662 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,
%T A275662 24,13,1,255,498,258,122,61,28,15,1,511,1026,551,261,136,71,32,17,1,
%U A275662 1023,2065,1163,531,298,157,81,36,19,1
%N A275662 Triangle read by rows: T(n,k) = number of convex domino towers with n dominoes having widest row with k dominoes.
%C A275662 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.
%H A275662 T. M. Brown, <a href="http://arxiv.org/abs/1608.01562">Convex domino towers</a>, arXiv:1608.01562 [math.CO] (2016).
%F A275662 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.
%e A275662 Triangle begins:
%e A275662 1;
%e A275662 3, 1;
%e A275662 7, 6, 1;
%e A275662 15, 18, 7, 1;
%e A275662 ...
%e A275662 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.
%Y A275662 Column 1: A000225, n>=1.
%Y A275662 Cf. A117468, A275204, A275599.
%K A275662 nonn,tabl,more
%O A275662 1,2
%A A275662 _Tricia Muldoon Brown_, Aug 04 2016