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A278319
Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 18 2016
STATUS
approved