Suresh Govindarajan - cp's OEIS frontend

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.

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.

A274598 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+4) rectangle.

Original entry on oeis.org

1, 5, 14, 40, 103, 247, 567, 1252, 2668, 5539, 11214, 22247, 43300, 82871, 156152, 290202, 532430, 965395, 1731351, 3073660, 5404984, 9420512, 16282463, 27922063, 47527430, 80331385, 134873275, 225015223, 373141724, 615224276, 1008792896, 1645443771, 2670372299, 4312780664, 6933014899

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, 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.

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.

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.

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

Original entry on oeis.org

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.

A244252 Total number of incoming edges at depth n in the solid partitions graph.

Original entry on oeis.org

1, 4, 16, 46, 128, 332, 842, 2042, 4846, 11146, 25114, 55310, 119662, 254354, 532784, 1100411, 2245118, 4528212, 9038898, 17868025, 35006932, 68008606, 131083778, 250774482, 476372848, 898837825, 1685107392, 3139812791, 5816015908, 10712596279, 19625001436, 35765137033, 64853219808, 117031972499, 210211082354, 375886565558, 669232663688, 1186538314110, 2095236499224, 3685445929502

Offset: 1

Suresh Govindarajan, Jun 23 2014

The solid partition graph is constructed as a directed graph whose vertices are solid partitions. The root vertex of the graph is the unique solid partition with one node. Given a solid partition, draw on outward directed edge to all solid partitions that can be obtained by the addition of a single node to the solid partition. The depth of a given vertex is given by the number of its nodes.

			a(2) = 4 as all four solid partitions of 2 are connected to the root vertex.

N. Destainville and S. Govindarajan, Estimating the asymptotics of solid partitions, arXiv:1406.5605 [cond-mat.stat-mech], 2014.

Cf. A000293, A090984, A000070.

A179855 Number of 8-dimensional partitions of n.

Original entry on oeis.org

1, 9, 45, 201, 819, 3231, 12321, 46209, 170370, 621316, 2240838, 8011584, 28395213, 99845553, 348333411, 1205925033, 4142850423

Offset: 1

Suresh Govindarajan, Jan 11 2011

nonn

Andrews, George E., The Theory of Partitions, Cambridge University Press, 1984. Cambridge Books Online. Cambridge University Press.

Cf. A000041, A000219, A000293, A000334, A000390, A000416, A000427, A096651.

cp's OEIS Frontend

User: Suresh Govindarajan

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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A274598 Number of ways to remove n oranges from an infinite stack of oranges whose m-th layer is an m X (m+4) 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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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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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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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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A244252 Total number of incoming edges at depth n in the solid partitions graph.

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A179855 Number of 8-dimensional partitions of n.

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