A204650 Number of (n+1) X 8 0..1 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) nondecreasing in column and row directions, respectively.

216, 283, 637, 1478, 3261, 6780, 13314, 24862, 44426, 76378, 126906, 204583, 321038, 491781, 737163, 1083525, 1564519, 2222657, 3111073, 4295556, 5856841, 7893218, 10523448, 13890048, 18162936, 23543500, 30269084, 38617957, 48914760, 61536499

Offset

1,1

Comments

Column 7 of A204651.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 48*a(n-3) - 42*a(n-4) + 42*a(n-6) - 48*a(n-7) + 27*a(n-8) - 8*a(n-9) + a(n-10) for n > 15.

Empirical g.f.: x*(216 - 1445*x + 4205*x^2 - 6345*x^3 + 4124*x^4 + 1908*x^5 - 6141*x^6 + 5440*x^7 - 2472*x^8 + 519*x^9 + 27*x^10 - 28*x^11 - 24*x^12 + 24*x^13 - 6*x^14) / ((1 - x)^9*(1 + x)). - Colin Barker, Jun 08 2018

Example

Some solutions for n=5:
  1 0 1 0 1 0 0 1       0 0 0 0 0 0 0 0       0 0 0 0 0 0 0 1
  0 1 0 1 0 1 1 1       0 0 0 0 0 0 0 1       0 0 0 0 0 0 0 1
  1 0 1 0 1 1 1 1       0 0 0 0 0 0 0 1       0 0 0 0 0 0 1 1
  0 1 0 1 1 1 1 1       0 0 0 1 1 1 1 1       0 0 0 0 0 1 1 1
  1 0 1 1 1 1 1 1       1 1 1 1 1 1 1 1       0 0 0 0 0 1 1 1
  0 1 1 1 1 1 1 1       1 1 1 1 1 1 1 1       1 1 1 1 1 1 1 1

Crossrefs

Cf. A204651.

Sequence in context: A184088 A348609 A205191 * A115430 A278976 A179419

Adjacent sequences: A204647 A204648 A204649 * A204651 A204652 A204653

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved