A202027 Number of n X 2 zero-sum -1..1 arrays with rows and columns lexicographically nondecreasing.

2, 7, 21, 56, 130, 281, 555, 1034, 1827, 3090, 5028, 7929, 12143, 18144, 26512, 37981, 53440, 74001, 100965, 135932, 180770, 237705, 309317, 398656, 509191, 644982, 810632, 1011433, 1253353, 1543214, 1888620, 2298205, 2781564, 3349469, 4013843

Offset

1,1

Comments

Column 2 of A202033.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -6*a(n-3) +6*a(n-5) +7*a(n-6) -9*a(n-7) -9*a(n-8) +7*a(n-9) +6*a(n-10) -6*a(n-12) +3*a(n-14) -a(n-15).

Empirical g.f.: x*(2 + x + 5*x^3 + 4*x^4 + 5*x^5 - 8*x^6 - 8*x^7 + 9*x^8 + 5*x^9 - 2*x^10 - 5*x^11 + 3*x^13 - x^14) / ((1 - x)^8*(1 + x)^3*(1 + x + x^2)^2). - Colin Barker, May 25 2018

Example

Some solutions for n=10:
.-1.-1...-1.-1...-1.-1...-1..0...-1.-1...-1.-1...-1.-1...-1.-1...-1.-1...-1..0
.-1..1...-1.-1...-1.-1...-1..0...-1..1...-1.-1...-1..1...-1.-1...-1.-1...-1..0
.-1..1...-1.-1...-1.-1....0.-1....0..0...-1.-1...-1..1...-1.-1...-1..1...-1..0
.-1..1...-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0....0..1
..0.-1....0..1....0..1....0..0....0..1....0..0...-1..1....0..1....0..0....1.-1
..0..1....0..1....1.-1....0..0....0..1....0..1...-1..1....0..1....1.-1....1.-1
..0..1....0..1....1..0....0..0....1.-1....0..1....0..0....0..1....1.-1....1.-1
..1.-1....0..1....1..0....1.-1....1.-1....0..1....0..0....0..1....1..0....1.-1
..1.-1....1.-1....1..0....1..0....1.-1....0..1....0..0....0..1....1..0....1.-1
..1..0....1..1....1..1....1..1....1.-1....1..1....1..1....1..0....1..1....1..1

Crossrefs

Cf. A202033.

Sequence in context: A212338 A246861 A305601 * A374958 A018036 A007050

Adjacent sequences: A202024 A202025 A202026 * A202028 A202029 A202030

Keyword

nonn

Author

R. H. Hardin, Dec 09 2011

Status

approved