A255993 Number of length n+2 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

8, 16, 28, 45, 68, 98, 136, 183, 240, 308, 388, 481, 588, 710, 848, 1003, 1176, 1368, 1580, 1813, 2068, 2346, 2648, 2975, 3328, 3708, 4116, 4553, 5020, 5518, 6048, 6611, 7208, 7840, 8508, 9213, 9956, 10738, 11560, 12423, 13328, 14276, 15268, 16305

Offset: 1

Author

R. H. Hardin, Mar 13 2015

Keywords

• nonn

Comments

Row 2 of A255992.

Let T(n,k) = n*k + binomial(k+n, n+1), then A001477 (n=0), A000096 (n=1), and presumably this sequence (n=2). Seen this way a(0)=0, a(1)=3 and the offset here should be 2 (as is also hinted by the name: "Number of length n+2 .."). - Peter Luschny, Aug 25 2019

Examples

			Some solutions for n=4:
  0  0  0  1  0  0  1  1  0  0  1  0  0  1  1  1
  0  1  1  1  0  1  1  0  1  0  1  1  0  0  1  1
  0  1  1  0  0  1  1  0  0  0  1  0  1  0  1  1
  0  0  1  0  1  0  1  0  1  1  0  0  1  1  0  1
  1  1  1  1  1  0  1  0  1  0  1  1  1  1  0  0
  1  1  1  1  0  0  0  0  1  0  1  1  0  1  0  0
		

Links

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

Crossrefs

Cf. A255992.

Formula

Empirical: a(n) = (1/6)*n^3 + n^2 + (23/6)*n + 3.

Empirical g.f.: x*(2 - x)*(4 - 6*x + 3*x^2) / (1 - x)^4. - Colin Barker, Jan 25 2018

Empirical: a(n) = A000292(n+3) - A000124(n+1). - Torlach Rush, Aug 04 2018