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Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+2) rectangle.
6

%I #27 Jul 10 2016 22:48:59

%S 1,3,7,19,44,98,213,448,918,1832,3584,6882,13012,24220,44480,80678,

%T 144697,256775,451305,786008,1357414,2325540,3954366,6676369,11196599,

%U 18657454,30901434,50884452,83327163,135733071,219978688,354780782,569519349,910130189,1448166991,2294680459

%N Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+2) rectangle.

%C This problem was stated in this fashion by R. Kenyon and Ben Young in the Domino Forum (domino@listserv.uml.edu).

%H Suresh Govindarajan, <a href="/A274596/b274596.txt">Table of n, a(n) for n = 0..45</a>

%H S. Govindarajan, A. J. Guttmann and V. Subramanyan, <a href="https://arxiv.org/abs/1607.01890">On a square-ice analogue of plane partitions</a>, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

%Y Cf. A274582, A274594, A274597, A274598, A274599.

%K nonn,hard

%O 0,2

%A _Suresh Govindarajan_, Jun 30 2016