A129876 Sequence i_n arising in enumeration of arrays of directed blocks (see Quaintance reference for precise definition).

2, 4, 14, 52, 210, 888, 3886, 17448, 79922, 372012, 1754526, 8366316, 40267426, 195365104, 954454750, 4691436944, 23184133474, 115120702740, 574085981614, 2873935425188, 14437612051570, 72760418799848, 367753953183246, 1863706441704888, 9468119928904850, 48209730517343548

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Jocelyn Quaintance, Letter Representations of m x n x p Proper Arrays, arXiv:math/0412244 [math.CO], 2004-2006. See Table 1.

Jocelyn Quaintance, Combinatoric Enumeration of Two-Dimensional Proper Arrays, Discrete Math., 307 (2007), 1844-1864. See Table 1.

Formula

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

The generating function A(x) satisfies: x^2*A(x)^3 + (x^2 - 2*x)*A(x)^2 + (x^2 - 2*x + 1)*A(x) - 2*x = 0. - Thomas Scheuerle, Jan 14 2026

Prog

(PARI) lista(m) = {my(A = t*O(t)); for (n= 1, m+1, A = t*(1+A)*(2-t*A)/((1-t*A)^2); ); return(vector(m, i, polcoeff(A, i, t))); } \\ Thomas Scheuerle, Jan 14 2026

Crossrefs

Cf. A129873-A129886.

Sequence in context: A003500 A316363 A295760 * A038055 A006385 A322859

Adjacent sequences: A129873 A129874 A129875 * A129877 A129878 A129879

Keyword

nonn

Author

N. J. A. Sloane, May 26 2007

Extensions

More terms from Thomas Scheuerle, Jan 14 2026

Status

approved