A225895 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.

7, 33, 145, 545, 1770, 5052, 12910, 30055, 64701, 130387, 248427, 451117, 785840, 1320222, 2148504, 3399307, 5244979, 7912725, 11697733, 16978521, 24234742, 34067696, 47223810, 64621359, 87380713, 116858407, 154685343, 202809445

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/3360)*n^8 + (3/560)*n^7 + (5/144)*n^6 + (7/120)*n^5 + (761/1440)*n^4 + (81/80)*n^3 + (122/63)*n^2 + (89/210)*n + 3.

Conjectures from Colin Barker, Sep 05 2018: (Start)

G.f.: x*(7 - 30*x + 100*x^2 - 160*x^3 + 195*x^4 - 162*x^5 + 82*x^6 - 23*x^7 + 3*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Column 3 of A225900.

Sequence in context: A372878 A141291 A278027 * A089106 A211829 A227555

Adjacent sequences: A225892 A225893 A225894 * A225896 A225897 A225898

Keyword

nonn

Author

R. H. Hardin, May 20 2013

Status

approved