

A264048


Triangle read by rows: T(n,k) (n>=1, k>=1) is the number of integer partitions lambda of n such that there are k compositions mu such that the GelfandTsetlin polytope for lambda and mu is integral.


3



1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1
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OFFSET

1,57


COMMENTS

Row sums give A000041, n >= 1.


LINKS

Table of n, a(n) for n=1..101.
FindStat  Combinatorial Statistic Finder, Number of integral GelfandTsetlin polytopes with prescribed top row and integer composition weight.
J. De Loera and T. B. McAllister, Vertices of GelfandTsetlin polytopes, arXiv:math/0309329 [math.CO], 2003, MathSciNet:2096742.


EXAMPLE

Triangle begins:
1,
1,1,
1,0,1,1,
1,0,0,1,1,0,1,1,
1,0,0,0,1,0,1,0,0,0,1,1,0,0,1,1,
1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,1,0,0,2,0,0,0,0,1,1,
...


CROSSREFS

Cf. A000041, A264035, A264047, A264049.
Sequence in context: A266344 A174875 A193510 * A101257 A321892 A225542
Adjacent sequences: A264045 A264046 A264047 * A264049 A264050 A264051


KEYWORD

nonn,tabf


AUTHOR

Christian Stump, Nov 02 2015


STATUS

approved



