A204644 Number of (n+1) X 2 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.

8, 16, 28, 48, 80, 132, 216, 352, 572, 928, 1504, 2436, 3944, 6384, 10332, 16720, 27056, 43780, 70840, 114624, 185468, 300096, 485568, 785668, 1271240, 2056912, 3328156, 5385072, 8713232, 14098308, 22811544, 36909856, 59721404, 96631264, 156352672, 252983940

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2, 0, -1) (empirical).

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3).

From the empirical recurrence, a(n) = 4*(Fibonacci(n + 3) - 1). - Ehren Metcalfe, Apr 04 2019

Example

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

Crossrefs

Column 1 of A204651.

Sequence in context: A045237 A255993 A299644 * A191271 A047925 A332918

Adjacent sequences: A204641 A204642 A204643 * A204645 A204646 A204647

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved