A129880 Sequence d_n arising in enumeration of arrays of directed blocks (see Quaintance reference for precise definition).

1, 1, 4, 10, 32, 101, 334, 1129, 3890, 13618, 48275, 172995, 625574, 2279997, 8366553, 30885640, 114620926, 427383918, 1600323161, 6015226752, 22687991095, 85843131701, 325734335544, 1239274254094, 4726359853214, 18065978123065

Offset: 1

Author

N. J. A. Sloane, May 26 2007

Keywords

• nonn

Links

• Jocelyn Quaintance, Combinatoric Enumeration of Two-Dimensional Proper Arrays, Discrete Math., 307 (2007), 1844-1864.

Programs

PARI

listdn(m) = { my(D = t*O(t)); for (n= 1, m, D = (t - (t^3 + t^2)*D^3 - (t^3 - t^2 - 2*t)*D^2)/(1 - t - t^2);); return(vector(m, i , polcoeff(D, i, t)));} \\ Michel Marcus, Mar 29 2013

Formula

See Quaintance reference for generating functions that produce A129872-A129886.

G.f.: D(t) satisfies (t^3 + t^2)*D^3 + (t^3 - t^2 - 2*t)*D^2 + (-t^2 - t + 1)*D - t = 0. Michel Marcus, Mar 29 2013