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

1,2

Links

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

Formula

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)

Example

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

Crossrefs

Column 2 of A278325.

Sequence in context: A363603 A092786 A015529 * A305203 A246150 A000948

Adjacent sequences: A278316 A278317 A278318 * A278320 A278321 A278322

Keyword

nonn

Author

R. H. Hardin, Nov 18 2016

Status

approved