A203780 Number of (n+1) X 2 0..3 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) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.

90, 565, 3352, 18332, 93578, 452825, 2103364, 9466880, 41577146, 179125413, 760104672, 3186880092, 13234285226, 54540491961, 223403152908, 910633752400, 3697500096250, 14966619506101, 60431546809704, 243527111738236

Offset

1,1

Comments

Column 1 of A203787.

Links

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

Formula

Empirical: a(n) = 18*a(n-1) -139*a(n-2) +604*a(n-3) -1627*a(n-4) +2818*a(n-5) -3141*a(n-6) +2176*a(n-7) -852*a(n-8) +144*a(n-9).

Empirical g.f.: x*(90 - 1055*x + 5692*x^2 - 17829*x^3 + 34700*x^4 - 42404*x^5 + 31552*x^6 - 13056*x^7 + 2304*x^8) / ((1 - x)^4*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)). - Colin Barker, Jun 04 2018

Example

Some solutions for n=4:
..0..2....1..3....1..1....2..1....1..2....3..1....0..3....1..0....0..1....2..0
..1..3....1..3....1..1....2..3....1..3....1..3....0..3....0..1....3..2....0..2
..2..2....3..1....2..2....2..3....1..3....1..3....1..2....0..3....2..3....1..1
..1..3....1..3....2..3....2..3....3..2....1..3....1..3....1..2....3..2....3..1
..2..2....1..3....2..3....2..3....2..3....3..2....3..3....1..2....2..3....1..3

Crossrefs

Cf. A203787.

Sequence in context: A156738 A211446 A203787 * A295982 A065949 A224541

Adjacent sequences: A203777 A203778 A203779 * A203781 A203782 A203783

Keyword

nonn

Author

R. H. Hardin, Jan 05 2012

Status

approved