A233402 Number of (n+1) X (1+1) 0..2 arrays with row and column sums nondecreasing, and no adjacent elements equal.

9, 11, 22, 24, 41, 42, 66, 65, 97, 93, 134, 126, 177, 164, 226, 207, 281, 255, 342, 308, 409, 366, 482, 429, 561, 497, 646, 570, 737, 648, 834, 731, 937, 819, 1046, 912, 1161, 1010, 1282, 1113, 1409, 1221, 1542, 1334, 1681, 1452, 1826, 1575, 1977, 1703, 2134

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).

Conjectures from Colin Barker, Oct 11 2018: (Start)

G.f.: x*(9 + 11*x - 5*x^2 - 9*x^3 + 2*x^4 + 3*x^5) / ((1 - x)^3*(1 + x)^3).

a(n) = (62 - 14*(-1)^n + (50-6*(-1)^n)*n + (11+(-1)^(1+n))*n^2) / 16.

(End)

Example

Some solutions for n=5:
..2..0....0..1....0..1....1..0....0..1....0..2....0..1....1..0....1..0....0..1
..0..2....1..0....1..0....0..2....1..0....2..0....1..0....0..1....0..1....1..0
..2..0....0..2....0..2....2..0....0..1....0..2....0..2....1..0....2..0....2..1
..0..2....2..0....2..0....1..2....1..0....2..1....2..1....0..2....0..2....1..2
..2..1....0..2....0..2....2..1....2..1....1..2....1..2....2..1....2..1....2..1
..1..2....2..1....2..0....1..2....1..2....2..1....2..1....1..2....1..2....1..2

Crossrefs

Column 1 of A233408.

Sequence in context: A022323 A106525 A103510 * A276406 A130730 A153697

Adjacent sequences: A233399 A233400 A233401 * A233403 A233404 A233405

Keyword

nonn

Author

R. H. Hardin, Dec 09 2013

Status

approved