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.
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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
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)
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