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

0,3

Comments

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

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.

Example

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.

Crossrefs

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

Sequence in context: A128516 A022569 A093831 * A052365 A107659 A162588

Adjacent sequences: A274579 A274580 A274581 * A274583 A274584 A274585

Keyword

nonn,hard

Author

Suresh Govindarajan, Jun 30 2016

Status

approved