A202936 Number of (n+3) X 8 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.

160000, 273683, 481798, 857408, 1515902, 2631416, 4457228, 7350643, 11802908, 18474721, 28237922, 42223978, 61879898, 89032238, 125959880, 175476293, 241022008, 326768063, 437731198, 579901604, 760384054, 987553268, 1271224388

Offset

1,1

Comments

Column 5 of A202939.

Links

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

Formula

Empirical: a(n) = (1/1680)*n^8 + (17/210)*n^7 + (134/45)*n^6 + (256/5)*n^5 + (352481/720)*n^4 + (55381/20)*n^3 + (32201731/2520)*n^2 + (19670981/420)*n + 97073.

Conjectures from Colin Barker, Jun 03 2018: (Start)

G.f.: x*(160000 - 1166317*x + 3778651*x^2 - 7066186*x^3 + 8314586*x^4 - 6291988*x^5 + 2987174*x^6 - 812969*x^7 + 97073*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=1:
..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..1....0..0..0..0..0..0..0..0
..0..0..0..0..1..1..0..0....0..0..0..0..1..1..1..0....0..0..0..0..0..0..0..1
..0..0..0..0..0..1..1..1....0..0..0..0..1..0..0..0....0..0..0..0..0..1..1..1
..0..0..0..0..1..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..1..0

Crossrefs

Cf. A202939.

Sequence in context: A268910 A223286 A223483 * A251971 A013897 A205742

Adjacent sequences: A202933 A202934 A202935 * A202937 A202938 A202939

Keyword

nonn

Author

R. H. Hardin, Dec 26 2011

Status

approved