A129872 Sequence M_n arising in enumeration of arrays of directed blocks (see 2007 Quaintance reference for precise definition). [The next term is not an integer.]

1, 4, 16, 72, 364, 1916, 10581, 59681, 343903, 2010089

Offset

1,2

Comments

Warning: as defined the terms are not integral in general: 1, 4, 16, 72, 364, 1916, 10581, 59681, 343903, 2010089, 23798969/2, ... - Jocelyn Quaintance, Mar 31 2013.

Links

Table of n, a(n) for n=1..10.

Jocelyn Quaintance, Letter Representations of m x n x p Proper Arrays (2004), arXiv:math/0412244. 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.

Prog

(PARI) listrn(m) = {R = t*O(t); for (n= 1, m, R = (2*t^11 + t^10 + 3*t^9 + 8*t^8 + 12*t^7 + 16*t^6 + 26*t^5 + 20*t^4 + 16*t^3 + 7*t^2 + t - (t^14 - t^12 - 8*t^10 - 11*t^8 - 5*t^6 + t^4)*R^3 - (3*t^13 + t^12 - 5*t^11 - 2*t^10 - 34*t^9 - 14*t^8 - 39*t^7 - 16*t^6 - 11*t^5 - 2*t^4 + 6*t^3 + 2*t^2)*R^2)/(t^12 + t^11 - 7*t^10 - 7*t^9 - 42*t^8 - 35*t^7 - 51*t^6 - 41*t^5 - 14*t^4 - 4*t^3 + 8*t^2 + 6*t + 1); ); return(vector(m, i , polcoeff(R, i, t))); }
listbn(m) = {B = t*O(t); for (n= 1, m, B = (1 + 2*t*B^2 - t^2*B^3 ); ); return(vector(m, i , polcoeff(B, i, t))); }
listMn(m) = {b = listbn(m); /* see also A006013 */ s = listsn(m); /* see A129873 */ d = listdn(m); /* see A129880 */ r = listrn(m); for (i=1, m, v = (b[i] + s[i] - d[i] - r[i])/2; print1(v, ", "); ); }
\\ Michel Marcus, Mar 30 2013

Crossrefs

Cf. A129873-A129886.

Sequence in context: A152807 A217461 A370276 * A059371 A208528 A007234

Adjacent sequences: A129869 A129870 A129871 * A129873 A129874 A129875

Keyword

nonn

Author

N. J. A. Sloane, May 26 2007

Extensions

Edited by N. J. A. Sloane, Nov 29 2016

Status

approved