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A275599 Triangle read by rows: T(n,k) = number of right-skewed domino towers with n dominoes having a base of k dominoes placed end-to-end.

%I A275599 #27 Aug 15 2016 20:39:24
%S A275599 1,3,1,7,4,1,15,12,4,1,31,27,13,4,1,63,61,34,13,4,1,127,124,77,35,13,
%T A275599 4,1,255,258,165,86,35,13,4,1,511,513,348,185,87,35,13,4,1,1023,1039,
%U A275599 698,399,196,87,35,13,4,1,2047,2062,1410,811,423,197,87,35,13,4,1
%N A275599 Triangle read by rows: T(n,k) = number of right-skewed domino towers with n dominoes having a base of k dominoes placed end-to-end.
%C A275599 Domino towers are created by stacking domino blocks horizontally on a convex base of k dominoes.  A right-skewed domino tower is a parallelogram domino tower such that at least one column of the polyomino is to the right of the base.
%H A275599 T. M. Brown <a href="http://arxiv.org/abs/1608.01562">Convex domino towers</a>, arXiv:1608.01562 [math.CO], (2016)
%H A275599 Tricia Muldoon Brown, <a href="/A275599/a275599.pdf">Examples of right- or left-skewed domino towers of 10 dominoes having a base of 4 dominoes</a>
%F A275599 T(n,k) = Sum_{i=1..k} 2*T(n-k,i)+A(n-k,i) where A(n,k) is given by A275204 and with initial conditions T(n+1,n)=1 and T(n,k)=0 if n<2 and k<1, or n<k+1.
%F A275599 G.f.: x^k/(1-2x^k) Sum_{i=1..k}*A_k(x)*(Sum_{Subsets S of {i,i+1,..,k-1}} (Product_{j in S} 2x^j/(1-2x^k)) where A_k(x) is the generating function in A275204.
%e A275599 Triangle begins:
%e A275599 1;
%e A275599 3, 1;
%e A275599 7, 4, 1;
%e A275599 15, 12, 4, 1;
%e A275599 ...
%e A275599 For n = 5 and k = 3, each tower has a convex base of three dominoes. The fourth domino may be placed directly above the rightmost domino of the base, in which case the fifth domino must be placed on the fourth domino so its right end is not above the base. Alternately, the fourth domino may be placed so its right end is not above the base, leaving three choices for the fifth domino: directly above, above and to the right, or directly to the left on the same level. Thus T(5,3) = 4.
%Y A275599 Column 1: A000225, n>=1.
%Y A275599 Cf. A275204.
%K A275599 nonn,tabl
%O A275599 2,2
%A A275599 _Tricia Muldoon Brown_, Aug 03 2016