A224190 -id:A224190 - cp's OEIS frontend

A224193 Number of 6Xn 0..2 arrays with rows unimodal and columns nondecreasing.

28, 784, 13524, 163746, 1519738, 11444292, 72710554, 400958714, 1960596602, 8643660124, 34817290272, 129528551708, 449030731802, 1461369918218, 4493166765659, 13121663640985, 36566337458326, 97628603745396

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 6 of A224190

			Some solutions for n=3
..0..1..1....0..1..0....0..0..0....0..1..1....0..0..0....0..0..0....0..1..0
..1..1..1....0..1..0....1..0..0....1..1..1....0..0..0....0..1..0....0..2..0
..1..2..1....1..1..1....1..0..0....2..1..1....0..0..0....1..1..1....1..2..1
..1..2..1....1..2..2....1..1..1....2..2..1....1..2..1....2..1..1....1..2..1
..2..2..1....2..2..2....2..1..1....2..2..2....1..2..1....2..2..2....2..2..1
..2..2..1....2..2..2....2..2..2....2..2..2....1..2..2....2..2..2....2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/35608838483312640000)*n^24 + (1/228261785149440000)*n^23 + (2993/8515157028618240000)*n^22 + (1189/64508765368320000)*n^21 + (112787/162193467211776000)*n^20 + (4033303/202741834014720000)*n^19 + (100023181/224083079700480000)*n^18 + (75069509/9336794987520000)*n^17 + (1246517053/10545086103552000)*n^16 + (6306246257/4393785876480000)*n^15 + (18213412351/1255367393280000)*n^14 + (38516770459/313841848320000)*n^13 + (9185104716379/10545086103552000)*n^12 + (1753572682469/337983528960000)*n^11 + (42653443424521/1647669703680000)*n^10 + (118327836601829/1098446469120000)*n^9 + (1768182454793/4763670912000)*n^8 + (698418986666497/666913927680000)*n^7 + (26428459959973901/11087444047680000)*n^6 + (31671555902461499/7391629365120000)*n^5 + (14625059352544909/2463876455040000)*n^4 + (438413487383/71292721500)*n^3 + (10755031442327/2248776129600)*n^2 + (2550558151/1338557220)*n + 1

A224184 Number of n X n 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

3, 36, 684, 15779, 408222, 11444292, 340780382, 10635858679, 344674481333, 11518916935288, 394956511554556, 13839075880034056, 494013661434533634, 17921279299283914328, 659361786079631903704, 24563166523294240335463

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Diagonal of A224190

			Some solutions for n=3
..0..1..0....0..1..0....2..0..0....0..0..2....0..0..1....1..0..0....0..2..0
..0..1..0....0..1..1....2..0..0....2..2..2....0..0..1....1..0..0....2..2..1
..1..2..0....1..1..1....2..1..1....2..2..2....1..1..2....2..0..0....2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..19

A224185 Number of n X 3 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

22, 158, 684, 2205, 5852, 13524, 28176, 54153, 97570, 166738, 272636, 429429, 655032, 971720, 1406784, 1993233, 2770542, 3785446, 5092780, 6756365, 8849940, 11458140, 14677520, 18617625, 23402106, 29169882, 36076348, 44294629, 54016880

Offset: 1

R. H. Hardin, Apr 01 2013

nonn

Column 3 of A224190.

			Some solutions for n=3.
..1..0..0....0..1..0....2..1..0....0..2..1....0..0..0....0..0..1....0..0..0
..2..0..0....1..2..0....2..2..0....0..2..1....1..0..0....0..0..2....1..1..0
..2..0..0....1..2..2....2..2..1....1..2..1....2..2..0....0..0..2....2..2..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A224190.

Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (205/72)*n^4 + (49/8)*n^3 + (319/45)*n^2 + (21/5)*n + 1.
Conjectures from Colin Barker, Aug 29 2018: (Start)
G.f.: x*(22 + 4*x + 40*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

46, 548, 3526, 15779, 55438, 163746, 424326, 992607, 2138488, 4305730, 8191976, 14853709, 25840868, 43366252, 70515252, 111501861, 171977322, 259398184, 383460946, 556610879, 794633026, 1117333790, 1549321930, 2120898195

Offset: 1

R. H. Hardin, Apr 01 2013

nonn

Column 4 of A224190.

			Some solutions for n=3:
..0..1..0..0....1..1..1..1....2..1..0..0....0..1..2..0....0..1..0..0
..1..1..0..0....1..1..1..1....2..1..1..0....0..2..2..0....0..1..1..0
..1..2..0..0....1..1..1..1....2..2..1..1....0..2..2..0....1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A224190.

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1.
Conjectures from Colin Barker, Aug 29 2018: (Start)
G.f.: x*(46 + 134*x + 250*x^2 - 91*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

A224187 Number of nX5 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

86, 1600, 14751, 89380, 408222, 1519738, 4844576, 13669953, 34953776, 82399174, 181434331, 376946128, 744873156, 1409068188, 2565196232, 4513845865, 7705502706, 12800568660, 20748212991, 32888515396, 51083111090, 77880377510

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 5 of A224190

			Some solutions for n=3
..0..1..0..0..0....0..1..2..1..1....0..0..1..1..1....0..1..2..1..1
..0..1..1..0..0....0..1..2..1..1....0..2..2..1..1....2..2..2..2..1
..1..2..2..2..2....0..1..2..2..2....0..2..2..1..1....2..2..2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1009/907200)*n^10 + (913/36288)*n^9 + (15121/60480)*n^8 + (8677/6048)*n^7 + (226987/43200)*n^6 + (110621/8640)*n^5 + (3804217/181440)*n^4 + (206081/9072)*n^3 + (130433/8400)*n^2 + (3793/630)*n + 1

A224188 Number of n X 6 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

148, 4102, 52591, 422488, 2469182, 11444292, 44435746, 150015321, 452158538, 1240740774, 3145970477, 7456438392, 16672410340, 35430409240, 71995370532, 140596619273, 264988109400, 483746928198, 857992826459, 1482422036736

Offset: 1

R. H. Hardin, Apr 01 2013

nonn

Column 6 of A224190.

			Some solutions for n=3:
..0..0..1..1..1..0....0..1..1..0..0..0....0..2..2..1..1..0....0..1..1..1..0..0
..0..1..1..1..2..1....0..1..1..2..0..0....0..2..2..2..1..0....1..1..2..2..2..0
..0..1..1..1..2..2....0..2..2..2..2..0....2..2..2..2..2..0....2..2..2..2..2..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (761/8553600)*n^12 + (811/302400)*n^11 + (98797/2721600)*n^10 + (105751/362880)*n^9 + (2800757/1814400)*n^8 + (429167/75600)*n^7 + (1442737/97200)*n^6 + (373033/13440)*n^5 + (100027061/2721600)*n^4 + (15191569/453600)*n^3 + (16485617/831600)*n^2 + (4273/630)*n + 1.

A224189 Number of nX7 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

239, 9503, 165212, 1727738, 12741432, 72710554, 340780382, 1366188661, 4823267213, 15322738603, 44529268480, 119909493132, 302279622352, 719306742780, 1626780581324, 3516536949577, 7300336446323, 14614022023815

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Column 7 of A224190

			Some solutions for n=3
..0..0..0..0..1..0..0....0..0..1..2..0..0..0....0..0..1..1..2..0..0
..0..1..1..2..1..1..0....0..0..1..2..1..0..0....0..2..2..2..2..1..1
..0..2..2..2..2..1..0....0..0..1..2..1..1..1....2..2..2..2..2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (118519/21794572800)*n^14 + (93527/444787200)*n^13 + (6343/1710720)*n^12 + (9456619/239500800)*n^11 + (1028647/3628800)*n^10 + (10525213/7257600)*n^9 + (5190079/952560)*n^8 + (47462621/3110400)*n^7 + (99470417/3110400)*n^6 + (542507339/10886400)*n^5 + (226284461/3991680)*n^4 + (453542611/9979200)*n^3 + (60780847/2522520)*n^2 + (96119/12870)*n + 1

A224191 Number of 4Xn 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

15, 225, 2205, 15779, 89380, 422488, 1727738, 6272940, 20614382, 62231446, 174603882, 459586532, 1143581612, 2707062766, 6128575771, 13328965295, 27955737041, 56730240471, 111704250407, 213954477597, 399506181220

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 4 of A224190

			Some solutions for n=3
..0..0..0....0..0..1....0..1..0....0..1..0....0..0..0....1..0..0....0..0..0
..0..0..1....0..0..1....0..2..0....0..2..0....0..0..0....1..0..0....1..0..0
..0..0..2....1..2..2....0..2..1....2..2..1....0..1..1....2..1..0....1..1..2
..0..1..2....1..2..2....0..2..2....2..2..2....0..2..2....2..1..0....2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/106748928000)*n^16 + (1/1482624000)*n^15 + (7/266872320)*n^14 + (127/197683200)*n^13 + (311999/28740096000)*n^12 + (212351/1596672000)*n^11 + (31937/26127360)*n^10 + (83129/9676800)*n^9 + (34840531/746496000)*n^8 + (9481183/48384000)*n^7 + (90994151/143700480)*n^6 + (123257231/79833600)*n^5 + (43399375531/15567552000)*n^4 + (2360326763/648648000)*n^3 + (218135/61776)*n^2 + (581099/360360)*n + 1

A224192 Number of 5Xn 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

21, 441, 5852, 55438, 408222, 2469182, 12741432, 57644194, 233385140, 859145920, 2912085006, 9181289736, 27151590510, 75840301088, 201262238349, 509972027785, 1239109721281, 2897739996141, 6543276177902, 14306873805792, 30366198279340

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 5 of A224190

			Some solutions for n=3
..1..2..0....0..1..0....0..1..0....0..0..0....0..2..1....0..0..2....1..1..0
..1..2..0....1..1..1....0..1..0....0..0..0....0..2..1....0..1..2....1..1..0
..2..2..0....2..1..1....0..1..2....1..2..1....0..2..1....1..2..2....2..2..0
..2..2..1....2..2..1....0..2..2....1..2..1....1..2..2....1..2..2....2..2..1
..2..2..2....2..2..2....1..2..2....2..2..2....1..2..2....2..2..2....2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/1379196149760000)*n^20 + (1/12538146816000)*n^19 + (467/101624979456000)*n^18 + (223/1302884352000)*n^17 + (9641/2134978560000)*n^16 + (44237/498161664000)*n^15 + (115879/86102016000)*n^14 + (24029081/1494484992000)*n^13 + (623419/4055040000)*n^12 + (18199033/15328051200)*n^11 + (3421967251/459841536000)*n^10 + (263944057/6967296000)*n^9 + (8168948285977/52306974720000)*n^8 + (193145489021/373621248000)*n^7 + (507138710909/373621248000)*n^6 + (13262560631/4790016000)*n^5 + (3783062210933/882161280000)*n^4 + (108121887773/22054032000)*n^3 + (27314271011/6518191680)*n^2 + (14737223/8314020)*n + 1

A224194 Number of 7Xn 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

36, 1296, 28176, 424326, 4844576, 44435746, 340780382, 2249643632, 13068669308, 67970305364, 320903298144, 1390873688506, 5586138847981, 20953028554541, 73888808853350, 246365532350644, 780525967950004, 2359724042194860

Offset: 1

R. H. Hardin Apr 01 2013

nonn

Row 7 of A224190

			Some solutions for n=3
..0..1..0....0..0..0....0..0..0....0..1..0....0..0..0....2..0..0....0..0..0
..0..1..0....0..0..0....0..1..0....1..2..0....0..0..0....2..0..0....0..1..1
..0..1..0....0..1..1....0..1..1....1..2..0....0..2..1....2..0..0....0..1..1
..0..1..1....1..1..1....0..1..1....1..2..2....2..2..1....2..1..0....0..2..1
..0..1..1....1..2..2....0..1..1....1..2..2....2..2..1....2..2..1....0..2..1
..1..2..1....2..2..2....0..2..2....1..2..2....2..2..1....2..2..1....0..2..2
..1..2..1....2..2..2....2..2..2....2..2..2....2..2..1....2..2..2....0..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 28

Empirical polynomial of degree 28 (see link above)

cp's OEIS Frontend

A224193 Number of 6Xn 0..2 arrays with rows unimodal and columns nondecreasing.

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A224184 Number of n X n 0..2 arrays with rows unimodal and columns nondecreasing.

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A224185 Number of n X 3 0..2 arrays with rows unimodal and columns nondecreasing.

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A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.

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A224187 Number of nX5 0..2 arrays with rows unimodal and columns nondecreasing.

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A224188 Number of n X 6 0..2 arrays with rows unimodal and columns nondecreasing.

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A224189 Number of nX7 0..2 arrays with rows unimodal and columns nondecreasing.

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A224191 Number of 4Xn 0..2 arrays with rows unimodal and columns nondecreasing.

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A224192 Number of 5Xn 0..2 arrays with rows unimodal and columns nondecreasing.

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A224194 Number of 7Xn 0..2 arrays with rows unimodal and columns nondecreasing.

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