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 A255994 Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs. 1

%I #8 Jan 25 2018 12:00:13

%S 16,32,53,80,114,156,207,268,340,424,521,632,758,900,1059,1236,1432,

%T 1648,1885,2144,2426,2732,3063,3420,3804,4216,4657,5128,5630,6164,

%U 6731,7332,7968,8640,9349,10096,10882,11708,12575,13484,14436,15432,16473,17560

%N Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 3 of A255992.

%H R. H. Hardin, <a href="/A255994/b255994.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/6)*n^3 + (3/2)*n^2 + (31/3)*n + 4.

%F Empirical g.f.: x*(16 - 32*x + 21*x^2 - 4*x^3) / (1 - x)^4. - _Colin Barker_, Jan 25 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015

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Last modified May 28 16:48 EDT 2024. Contains 372916 sequences. (Running on oeis4.)