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

1,1

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

Links

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

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

Example

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

Crossrefs

Cf. A255992.

Sequence in context: A331490 A039288 A045237 * A299644 A204644 A191271

Adjacent sequences: A255990 A255991 A255992 * A255994 A255995 A255996

Keyword

nonn

Author

R. H. Hardin, Mar 13 2015

Status

approved