A129873 Sequence s_n arising in enumeration of arrays of directed blocks (see Quaintance reference for precise definition).

2, 3, 8, 13, 38, 64, 196, 337, 1062, 1851, 5948, 10468, 34120, 60488, 199316, 355369, 1181126, 2115577, 7080928, 12731141, 42860534, 77306428, 261542752, 473018396, 1607076200, 2913321828, 9934255472, 18045744424, 61732449648, 112340143632

Offset: 1

Author

N. J. A. Sloane, May 26 2007

Keywords

• nonn

References

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

Programs

PARI

listsn(m) = {my(S = t*O(t)); for (n= 1, m+1, S = (- 8*t - 3 - (8*t^4 - t^2)*S^3 - (24*t^3 - 2*t^2 - 4*t)*S^2)/(24*t^2 + 2*t - 3);); return(vector(m, i , polcoeff(S, i, t)));} \\ Michel Marcus, Mar 29 2013

Formula

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

G.f.: S(t) satisfies (8*t^4 - t^2)*S(t)^3 + (24*t^3 - 2*t^2 - 4*t)*S(t)^2 + (24*t^2 + 2^t - 3)*S(t) + 8*t + 3 = 0. - Michel Marcus, Mar 29 2013

Extensions

More terms from Michel Marcus, Mar 29 2013