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A184545 Number of (n+2) X 8 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order. 1
415, 1114, 2413, 4774, 8989, 16345, 28844, 49489, 82648, 134509, 213640, 331669, 504100, 751282, 1099549, 1582550, 2242789, 3133396, 4320151, 5883784, 7922575, 10555279, 13924402, 18199855, 23583014, 30311215, 38662714, 48962143, 61586494 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Column 6 of A184548.
LINKS
FORMULA
Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (83/2880)*n^6 + (13/36)*n^5 + (15967/5760)*n^4 + (19201/1440)*n^3 + (121183/1120)*n^2 + (12673/56)*n + 64.
Conjectures from Colin Barker, Apr 13 2018: (Start)
G.f.: x*(415 - 2621*x + 7327*x^2 - 11699*x^3 + 11605*x^4 - 7310*x^5 + 2861*x^6 - 641*x^7 + 64*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
EXAMPLE
Some solutions for 4 X 8:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0
0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1
CROSSREFS
Cf. A184548.
Sequence in context: A332141 A187864 A190028 * A096032 A166057 A306381
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 16 2011
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)