A278778 -id:A278778 - cp's OEIS frontend

A278772 Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

0, 2, 20, 117, 503, 1750, 5209, 13751, 33000, 73282, 152581, 300872, 566293, 1023724, 1786462, 3021818, 4971616, 7978746, 12521114, 19254543, 29066411, 43142066, 63046335, 90822745, 129113400, 181302810, 251689347, 345688410, 470071817

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

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

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

Column 2 of A278778.

Empirical: a(n) = (1/3628800)*n^10 + (1/80640)*n^9 + (1/3780)*n^8 + (17/8064)*n^7 + (1513/172800)*n^6 + (167/11520)*n^5 + (12329/362880)*n^4 + (197/4032)*n^3 - (2167/50400)*n^2 - (11/168)*n.
Conjectures from Colin Barker, Feb 10 2019: (Start)
G.f.: x^2*(2 - 2*x + 7*x^2 - 14*x^3 + 12*x^4 - 5*x^5 + x^6) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)

A278773 Number of nX3 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

0, 20, 266, 1972, 10784, 48501, 189595, 665212, 2138149, 6384894, 17895624, 47447755, 119746565, 289136007, 670787381, 1500673676, 3247602855, 6817025467, 13912884597, 27665820296, 53701416899, 101922145950, 189427147850

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Column 3 of A278778.

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

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

Cf. A278778.

Empirical: a(n) = (1/121645100408832000)*n^19 + (1/800296713216000)*n^18 + (193/2134124568576000)*n^17 + (1/241416806400)*n^16 + (173/1280987136000)*n^15 + (26111/7846046208000)*n^14 + (12107647/188305108992000)*n^13 + (354047/362125209600)*n^12 + (113721193/9656672256000)*n^11 + (12542321/109734912000)*n^10 + (1257109487/1379524608000)*n^9 + (1427797621/241416806400)*n^8 + (1397907414289/47076277248000)*n^7 + (598789045909/5884534656000)*n^6 + (543697174847/2615348736000)*n^5 + (191422487/1005903360)*n^4 - (3436687523/44108064000)*n^3 - (46017833/154378224)*n^2 - (3115337/19399380)*n

A278774 Number of nX4 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

1, 117, 1972, 19750, 150085, 955347, 5355983, 27218249, 127644118, 559023840, 2305566900, 9009824325, 33520023813, 119176965881, 406212717567, 1330964850429, 4202125841615, 12811256626245, 37790376053439

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Column 4 of A278778.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 36

Cf. A278778.

Empirical polynomial of degree 36 (see link above)

A278775 Number of nX5 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

6, 503, 10784, 150085, 1673658, 16205001, 141166787, 1126917480, 8340736743, 57745890265, 376707516550, 2329550843590, 13722943412752, 77304542920321, 417679484040714, 2169521229525151, 10853156575543255, 52367994237483811

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Column 5 of A278778.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 69

Cf. A278778.

Empirical polynomial of degree 69 (see link above)

A278776 Number of nX6 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

21, 1750, 48501, 955347, 16205001, 251740932, 3634987413, 48847405083, 611199661843, 7140933364136, 78280456105686, 809842005695656, 7953581118077240, 74557744904209329, 670158115881138987

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Column 6 of A278778.

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

R. H. Hardin, Table of n, a(n) for n = 1..153
R. H. Hardin, Empirical polynomial of degree 134

Cf. A278778.

Empirical polynomial of degree 134 (see link above)

A278777 Number of nX7 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

56, 5209, 189595, 5355983, 141166787, 3634987413, 90752836672, 2155380363189, 48042054699217, 999491681597761, 19416161058987737, 353517442918850559, 6065787121333416262, 98680235108923294584, 1531317900358396738494

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Column 7 of A278778.

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

R. H. Hardin, Table of n, a(n) for n = 1..81

Cf. A278778.

A278771 Number of n X n 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Original entry on oeis.org

0, 2, 266, 19750, 1673658, 251740932, 90752836672, 93037538287080, 293564184229043556, 2953569640505846392444

Offset: 1

R. H. Hardin, Nov 28 2016

nonn

Diagonal of A278778.

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

Cf. A278778.

cp's OEIS Frontend

A278772 Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A278773 Number of nX3 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A278774 Number of nX4 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A278775 Number of nX5 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A278776 Number of nX6 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A278777 Number of nX7 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A278771 Number of n X n 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

Views

Author

Keywords

Comments

Examples

Crossrefs