

A275599


Triangle read by rows: T(n,k) = number of rightskewed domino towers with n dominoes having a base of k dominoes placed endtoend.


2



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, 4, 1, 255, 258, 165, 86, 35, 13, 4, 1, 511, 513, 348, 185, 87, 35, 13, 4, 1, 1023, 1039, 698, 399, 196, 87, 35, 13, 4, 1, 2047, 2062, 1410, 811, 423, 197, 87, 35, 13, 4, 1
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OFFSET

2,2


COMMENTS

Domino towers are created by stacking domino blocks horizontally on a convex base of k dominoes. A rightskewed domino tower is a parallelogram domino tower such that at least one column of the polyomino is to the right of the base.


LINKS

Table of n, a(n) for n=2..67.
T. M. Brown Convex domino towers, arXiv:1608.01562 [math.CO], (2016)
Tricia Muldoon Brown, Examples of right or leftskewed domino towers of 10 dominoes having a base of 4 dominoes


FORMULA

T(n,k) = Sum_{i=1..k} 2*T(nk,i)+A(nk,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/(12x^k) Sum_{i=1..k}*A_k(x)*(Sum_{Subsets S of {i,i+1,..,k1}} (Product_{j in S} 2x^j/(12x^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

Column 1: A000225, n>=1.
Cf. A275204.
Sequence in context: A086272 A104709 A110814 * A210038 A319076 A286513
Adjacent sequences: A275596 A275597 A275598 * A275600 A275601 A275602


KEYWORD

nonn,tabl


AUTHOR

Tricia Muldoon Brown, Aug 03 2016


STATUS

approved



