A274582 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X m square.

1, 1, 4, 10, 24, 51, 109, 222, 452, 890, 1732, 3298, 6204, 11470, 20970, 37842, 67572, 119368, 208943, 362389, 623438, 1064061, 1802976, 3033711, 5071418, 8424788, 13913192, 22847028, 37315678, 60631940, 98030644, 157743554, 252671288, 402944731, 639871871, 1011956958

Offset: 0

Author

Suresh Govindarajan, Jun 30 2016

Keywords

• nonn
• hard

Comments

This problem was stated in this fashion by R. Kenyon in the Domino Forum ([e-mail]).

Examples

			a(1)=1 as only the orange in the top layer can be removed. a(2)=4 as there are four oranges in the second layer and any one of them can be removed.
		

Links

• Suresh Govindarajan, Table of n, a(n) for n = 0..60
• S. Govindarajan, A. J. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

Crossrefs

Cf. A274594, A274596, A274597, A274598, A274599.