A278325 -id:A278325 - cp's OEIS frontend

A278319 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

0, 3, 20, 94, 395, 1492, 4991, 14848, 39832, 97835, 223015, 477126, 966849, 1869504, 3470210, 6214384, 10780448, 18178763, 29884150, 48010910, 75541039, 116618372, 176923705, 264148560, 388588200, 563877795, 807899313, 1143890790, 1601794149

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

			Some solutions for n=4:
..1..0. .0..1. .1..1. .1..0. .0..0. .1..1. .1..0. .1..1. .1..0. .1..0
..1..0. .0..0. .0..1. .1..1. .1..1. .0..1. .0..0. .0..1. .0..0. .1..1
..1..0. .1..0. .1..1. .0..1. .1..1. .0..0. .1..0. .0..0. .0..1. .1..1
..0..0. .0..1. .0..1. .0..1. .1..0. .1..0. .1..0. .0..0. .1..1. .1..0

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

Column 2 of A278325.

Empirical: a(n) = (1/39916800)*n^11 + (1/725760)*n^10 + (13/362880)*n^9 + (43/120960)*n^8 + (223/172800)*n^7 - (227/34560)*n^6 + (1019/45360)*n^5 + (27263/181440)*n^4 + (12193/113400)*n^3 - (121/840)*n^2 - (13/99)*n.
Conjectures from Colin Barker, Feb 09 2019: (Start)
G.f.: x^2*(3 - 16*x + 52*x^2 - 73*x^3 + 41*x^4 + x^5 - 10*x^6 + 3*x^7) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
(End)

A278320 Number of nX3 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

0, 20, 236, 1678, 9714, 51229, 251892, 1144205, 4762445, 18164685, 63838081, 208288721, 635843575, 1829104046, 4989647446, 12978273537, 32338548895, 77506161543, 179299342255, 401569610694, 873025241923, 1846627291485

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Column 3 of A278325.

			Some solutions for n=4
..1..0..1. .1..1..0. .0..0..0. .0..0..1. .0..1..0. .1..0..1. .0..0..0
..1..1..1. .0..1..0. .0..1..0. .1..0..0. .0..1..1. .1..0..1. .1..1..0
..1..0..1. .0..1..1. .0..0..1. .1..1..1. .0..0..1. .1..0..0. .1..1..0
..1..0..1. .1..1..1. .1..1..1. .0..0..1. .0..1..0. .1..1..1. .0..0..0

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

Cf. A278325.

Empirical: a(n) = (1/25852016738884976640000)*n^23 + (1/102181884343418880000)*n^22 + (1/858671297003520000)*n^21 + (1259/14597412049059840000)*n^20 + (3617/810967336058880000)*n^19 + (1831/10670622842880000)*n^18 + (13746263/2688996956405760000)*n^17 + (19040863/158176291553280000)*n^16 + (101471197/45193226158080000)*n^15 + (1480973341/45193226158080000)*n^14 + (61001884543/165708495912960000)*n^13 + (3617038307/1158800670720000)*n^12 + (1537519018181/79088145776640000)*n^11 + (13469195909881/158176291553280000)*n^10 + (4270693429711/11298306539520000)*n^9 + (9457223412823/2824576634880000)*n^8 + (218151538495819/8002967132160000)*n^7 + (775352818331437/8002967132160000)*n^6 + (627425471079349/3478413818880000)*n^5 + (3995289195644399/14783258730240000)*n^4 + (6585215991983/43020065088000)*n^3 - (217394476291/586637251200)*n^2 - (1933447697/5354228880)*n

A278321 Number of nX4 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

1, 94, 1678, 19854, 186987, 1548002, 11947350, 87562135, 605431820, 3905165468, 23355599964, 129475795828, 667503759881, 3215875683718, 14555156486463, 62204964640341, 252211338710097, 974245904884957, 3598868691539578

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Column 4 of A278325.

			Some solutions for n=4
..0..1..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1. .1..1..0..1
..1..0..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..1. .1..1..0..1
..0..1..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..0. .1..1..0..1
..1..1..0..1. .1..1..1..1. .0..1..1..1. .0..0..0..0. .0..0..1..1

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

Cf. A278325.

Empirical polynomial of degree 47 (see link above)

A278322 Number of nX5 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

6, 395, 9714, 186987, 3058990, 43798840, 570738085, 7010453565, 82490704797, 927749763030, 9874571566773, 98622311006346, 920542037366117, 8028589976371346, 65570255252201804, 503146509213296224

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Column 5 of A278325.

			Some solutions for n=4
..0..1..1..1..1. .0..0..1..1..0. .0..0..0..0..0. .0..0..1..1..1
..0..0..0..0..1. .0..1..0..1..1. .1..0..0..1..1. .0..0..0..0..1
..0..1..1..0..0. .0..1..0..1..0. .0..0..1..0..1. .0..0..1..0..0
..1..0..0..0..0. .1..1..1..1..0. .1..0..1..0..1. .0..0..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 95

Cf. A278325.

Empirical polynomial of degree 95 (see link above)

A278323 Number of nX6 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

21, 1492, 51229, 1548002, 43798840, 1133034160, 26606146271, 577253086055, 11856994168275, 234252250004719, 4462457602929707, 81437338008292870, 1411665474225016752, 23098384621606953307, 355699829714059120732

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Column 6 of A278325.

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

R. H. Hardin, Table of n, a(n) for n = 1..150

Cf. A278325.

A278324 Number of nX7 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

56, 4991, 251892, 11947350, 570738085, 26606146271, 1159826452573, 46588303100299, 1741053359883624, 61687083048618477, 2105403821298913363, 69685735738121699248, 2231675758500253736280, 68674888544867993485304

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Column 7 of A278325.

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

R. H. Hardin, Table of n, a(n) for n = 1..79

Cf. A278325.

A278318 Number of n X n 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

Original entry on oeis.org

0, 3, 236, 19854, 3058990, 1133034160, 1159826452573, 3539023342110534, 33693644340398789900, 1032075934040317150939325

Offset: 1

R. H. Hardin, Nov 18 2016

nonn

Diagonal of A278325.

			Some solutions for n=4
..0..1..0..0. .0..1..0..1. .0..0..1..0. .0..0..1..0. .0..0..1..1
..0..1..0..0. .1..0..0..1. .0..1..1..0. .0..0..0..0. .1..1..0..0
..0..0..1..1. .0..0..0..0. .1..0..1..0. .0..1..0..1. .1..1..0..1
..1..0..0..1. .0..1..0..0. .0..1..0..1. .1..0..0..1. .1..0..0..0

Cf. A278325.

cp's OEIS Frontend

A278319 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278320 Number of nX3 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278321 Number of nX4 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278322 Number of nX5 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278323 Number of nX6 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278324 Number of nX7 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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A278318 Number of n X n 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

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