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

1,1

Comments

Column 3 of A263799.

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)

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

Cf. A058187, A263799.

Sequence in context: A208474 A363979 A187781 * A344608 A086530 A357215

Adjacent sequences: A263791 A263792 A263793 * A263795 A263796 A263797

Keyword

nonn

Author

R. H. Hardin, Oct 26 2015

Status

approved