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A204645 Number of (n+1) X 3 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively. 1
16, 32, 56, 90, 137, 200, 283, 390, 526, 696, 906, 1162, 1471, 1840, 2277, 2790, 3388, 4080, 4876, 5786, 6821, 7992, 9311, 10790, 12442, 14280, 16318, 18570, 21051, 23776, 26761, 30022, 33576, 37440, 41632, 46170, 51073, 56360, 62051, 68166, 74726, 81752 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A204651.

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).

Conjectures from Colin Barker, Jun 08 2018: (Start)

G.f.: x*(16 - 32*x + 8*x^2 + 26*x^3 - 23*x^4 + 6*x^5) / ((1 - x)^5*(1 + x)).

a(n) = (576 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n even.

a(n) = (582 + 704*n + 232*n^2 + 16*n^3 + 2*n^4)/96 for n odd.

(End)

EXAMPLE

Some solutions for n=5:

..0..0..0....0..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1

..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1

..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..1..1....0..1..1

..0..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..1..1

..0..0..1....0..1..1....0..1..1....0..0..1....1..1..1....1..1..1....0..1..1

..1..1..1....1..1..1....1..1..1....0..0..1....1..1..1....1..1..1....1..1..1

CROSSREFS

Cf. A204651.

Sequence in context: A260050 A224544 A255994 * A236323 A018923 A264901

Adjacent sequences:  A204642 A204643 A204644 * A204646 A204647 A204648

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 17 2012

STATUS

approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)