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A183409 Number of n X 2 binary arrays with each sum of a(1..i,1..j) no greater than i*j/2 and rows and columns in nondecreasing order. 1
2, 5, 8, 15, 21, 34, 44, 65, 80, 111, 132, 175, 203, 260, 296, 369, 414, 505, 560, 671, 737, 870, 948, 1105, 1196, 1379, 1484, 1695, 1815, 2056, 2192, 2465, 2618, 2925, 3096, 3439, 3629, 4010, 4220, 4641, 4872, 5335, 5588, 6095, 6371, 6924, 7224, 7825, 8150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A183413.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

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).

Conjecture: a(n) = (2*n^3+11*n^2+31*n+27+(n^2+n+5)*(-1)^n)/32. - Luce ETIENNE, Nov 18 2014

Empirical g.f.: x*(2 + 3*x - 3*x^2 - 2*x^3 + 3*x^4 + x^5 - x^6) / ((1 - x)^4*(1 + x)^3). - Colin Barker, Mar 29 2018

EXAMPLE

Some solutions for 4 X 2:

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

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

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

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

CROSSREFS

Cf. A183413.

Sequence in context: A309546 A261543 A307190 * A262867 A024808 A238619

Adjacent sequences:  A183406 A183407 A183408 * A183410 A183411 A183412

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 04 2011

STATUS

approved

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Last modified June 17 22:14 EDT 2021. Contains 345086 sequences. (Running on oeis4.)