A202334 Number of (n+1) X 8 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.

100, 368, 1112, 2906, 6800, 14588, 29174, 55057, 98958, 170614, 283766, 457370, 717062, 1096910, 1641488, 2408309, 3470656, 4920852, 6874012, 9472322, 12889892, 17338232, 23072402, 30397889, 39678266, 51343690, 65900298, 83940562

Offset

1,1

Comments

Column 7 of A202335.

Links

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

Formula

Empirical: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (67/1440)*n^6 + (59/120)*n^5 + (8927/2880)*n^4 + (1439/120)*n^3 + (140383/5040)*n^2 + (1243/35)*n + 21.

Conjectures from Colin Barker, May 28 2018: (Start)

G.f.: x*(100 - 532*x + 1400*x^2 - 2254*x^3 + 2366*x^4 - 1636*x^5 + 722*x^6 - 185*x^7 + 21*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=5:
  0 0 0 0 0 0 0 0    0 0 0 0 0 0 0 1    0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 1    0 0 0 0 0 0 1 1    0 0 0 0 0 0 1 1
  0 0 0 0 0 0 1 1    0 0 0 0 0 1 1 1    0 0 0 0 0 0 1 1
  0 0 0 0 0 0 1 1    0 0 0 0 0 1 1 1    0 0 1 1 1 1 1 1
  0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1    1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1    0 0 1 1 1 1 1 1    1 1 1 1 1 1 1 1

Crossrefs

Cf. A202335.

Sequence in context: A349181 A138668 A017174 * A250806 A250853 A017270

Adjacent sequences: A202331 A202332 A202333 * A202335 A202336 A202337

Keyword

nonn

Author

R. H. Hardin, Dec 17 2011

Status

approved