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A227638
Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.
1
3, 11, 39, 127, 377, 1014, 2518, 5844, 12790, 26582, 52769, 100547, 184661, 328068, 565582, 948764, 1552366, 2482688, 3888261, 5973327, 9014649, 13382250, 19564750, 28200044, 40112142, 56355074, 78264849, 107520547, 146215717, 196941352
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/90720)*n^9 - (1/6720)*n^8 + (73/15120)*n^7 - (9/160)*n^6 + (2869/4320)*n^5 - (4367/960)*n^4 + (66841/2835)*n^3 - (41101/560)*n^2 + (17105/126)*n - 108 for n>3.
Conjectures from Colin Barker, Sep 09 2018: (Start)
G.f.: x*(3 - 19*x + 64*x^2 - 128*x^3 + 172*x^4 - 167*x^5 + 151*x^6 - 154*x^7 + 151*x^8 - 107*x^9 + 49*x^10 - 13*x^11 + 2*x^12) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>13.
(End)
EXAMPLE
Some solutions for n=4:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..1
..0..0..1....0..0..0....0..1..1....0..1..0....0..1..0....0..0..0....0..0..0
..0..1..0....1..0..0....1..0..0....0..0..1....0..0..0....0..0..1....1..0..1
..0..1..0....0..0..1....0..1..0....1..0..1....0..1..0....0..0..0....0..0..0
CROSSREFS
Column 3 of A227641.
Sequence in context: A112674 A064086 A089579 * A166336 A002783 A289834
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 18 2013
STATUS
approved