A274598 -id:A274598 - cp's OEIS frontend

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

Suresh Govindarajan, Jun 30 2016

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

			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.

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.

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

A274594 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+1) rectangle.

Original entry on oeis.org

1, 2, 5, 12, 29, 64, 139, 286, 582, 1148, 2227, 4234, 7950, 14692, 26842, 48438, 86509, 152902, 267783, 464766, 800095, 1366512, 2316840, 3900502, 6523432, 10841282, 17909533, 29416966, 48055443, 78093926, 126276743, 203211038, 325518314, 519138982, 824414851, 1303853212, 2053981256

Offset: 0

Suresh Govindarajan, Jun 30 2016

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

Suresh Govindarajan, Table of n, a(n) for n = 0..50
S. Govindarajan, A. J. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

Cf. A274582, A274596, A274597, A274598, A274599.

A274596 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+2) rectangle.

Original entry on oeis.org

1, 3, 7, 19, 44, 98, 213, 448, 918, 1832, 3584, 6882, 13012, 24220, 44480, 80678, 144697, 256775, 451305, 786008, 1357414, 2325540, 3954366, 6676369, 11196599, 18657454, 30901434, 50884452, 83327163, 135733071, 219978688, 354780782, 569519349, 910130189, 1448166991, 2294680459

Offset: 0

Suresh Govindarajan, Jun 30 2016

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

Suresh Govindarajan, Table of n, a(n) for n = 0..45
S. Govindarajan, A. J. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

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

A274597 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+3) rectangle.

Original entry on oeis.org

1, 4, 10, 28, 68, 158, 350, 750, 1559, 3170, 6292, 12252, 23445, 44164, 81995, 150288, 272150, 487388, 863887, 1516592, 2638648, 4552488, 7792566, 13239698, 22336630, 37433466, 62337628, 103186612, 169824540, 277967860, 452594316, 733229626, 1182159039, 1897140990, 3031012912

Offset: 0

Suresh Govindarajan, Jun 30 2016

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

Suresh Govindarajan, Table of n, a(n) for n = 0..45
Domino Forum, Domino Home Page
S. Govindarajan, A. J. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

Cf. A274582, A274594, A274596, A274598, A274599.

A274599 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+5) rectangle.

Original entry on oeis.org

1, 6, 19, 56, 152, 378, 898, 2042, 4476, 9526, 19740, 39978, 79342, 154650, 296489, 560022, 1043404, 1919708, 3491081, 6280514, 11185375, 19734004, 34509347, 59847208, 102976946, 175877782, 298279841, 502496682, 841161007, 1399559416, 2315201903, 3808746574, 6232651705, 10147431024

Offset: 0

Suresh Govindarajan, Jun 30 2016

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

Suresh Govindarajan, Table of n, a(n) for n = 0..45
Domino Forum, Domino Home Page
S. Govindarajan, A. J. Guttmann and V. Subramanyan, On a square-ice analogue of plane partitions, arXiv:1607.01890 [cond-mat.stat-mech], 2016.

Cf. A274582, A274594, A274596, A274597, A274598.

cp's OEIS Frontend

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

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A274594 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+1) rectangle.

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A274596 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+2) rectangle.

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A274597 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+3) rectangle.

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A274599 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+5) rectangle.

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