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A263794
Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing.
2
3, 3, 7, 7, 14, 14, 25, 25, 41, 41, 63, 63, 92, 92, 129, 129, 175, 175, 231, 231, 298, 298, 377, 377, 469, 469, 575, 575, 696, 696, 833, 833, 987, 987, 1159, 1159, 1350, 1350, 1561, 1561, 1793, 1793, 2047, 2047, 2324, 2324, 2625, 2625, 2951, 2951, 3303, 3303
OFFSET
1,1
COMMENTS
Column 3 of A263799.
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
Empirical: a(n) = A058187(n-1) + floor((n+3)/2). - Filip Zaludek, Dec 14 2016
Conjectures from Colin Barker, Dec 14 2016: (Start)
a(n) = (n^3 + 6*n^2 + 32*n + 48)/48 for n even.
a(n) = (n^3 + 9*n^2 + 47*n + 87)/48 for n odd.
G.f.: x*(3 - 5*x^2 + 4*x^4 - x^6) / ((1 - x)^4*(1 + x)^3).
(End)
EXAMPLE
Some solutions for n = 5:
1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0
1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0
1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0
CROSSREFS
Sequence in context: A208474 A363979 A187781 * A344608 A086530 A357215
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 26 2015
STATUS
approved