OFFSET
2,2
COMMENTS
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.
LINKS
T. M. Brown Convex domino towers, arXiv:1608.01562 [math.CO], (2016)
FORMULA
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.
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.
EXAMPLE
Triangle begins:
1;
3, 1;
7, 4, 1;
15, 12, 4, 1;
...
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.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Tricia Muldoon Brown, Aug 03 2016
STATUS
approved