A255993 - OEIS

A255993

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

%I #21 Aug 25 2019 08:47:01

%S 8,16,28,45,68,98,136,183,240,308,388,481,588,710,848,1003,1176,1368,

%T 1580,1813,2068,2346,2648,2975,3328,3708,4116,4553,5020,5518,6048,

%U 6611,7208,7840,8508,9213,9956,10738,11560,12423,13328,14276,15268,16305

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

%C Row 2 of A255992.

%C 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

%H R. H. Hardin, <a href="/A255993/b255993.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(2 - x)*(4 - 6*x + 3*x^2) / (1 - x)^4. - _Colin Barker_, Jan 25 2018

%F Empirical: a(n) = A000292(n+3) - A000124(n+1). - _Torlach Rush_, Aug 04 2018

%e Some solutions for n=4:

%e 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1

%e 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1

%e 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1

%e 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1

%e 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0

%e 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015