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A227162 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order. 1
4, 18, 62, 193, 558, 1507, 3828, 9149, 20609, 43918, 88960, 172130, 319637, 572050, 990413, 1664308, 2722302, 4345275, 6783191, 10375943, 15578976, 22994469, 33408938, 47838207, 67580783, 94280764, 130001506, 177311376, 239383023 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/90720)*n^9 + (1/8064)*n^8 + (17/30240)*n^7 + (13/960)*n^6 - (131/4320)*n^5 + (181/384)*n^4 - (146161/90720)*n^3 + (171511/10080)*n^2 - (25129/504)*n + 58 for n>3.
Conjectures from Colin Barker, Sep 07 2018: (Start)
G.f.: x*(4 - 22*x + 62*x^2 - 97*x^3 + 98*x^4 - 56*x^5 + 32*x^6 - 70*x^7 + 123*x^8 - 113*x^9 + 55*x^10 - 13*x^11 + 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:
..1..1..1....1..1..1....1..0..0....1..0..0....1..0..0....0..0..0....0..0..0
..1..1..0....1..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
..1..1..0....1..1..1....0..0..1....0..0..0....0..0..1....0..1..1....0..1..0
..1..0..0....1..1..0....0..0..0....0..0..0....0..0..1....0..1..0....0..0..1
CROSSREFS
Column 3 of A227165.
Sequence in context: A192069 A073373 A292465 * A057414 A165910 A212766
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 03 2013
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)