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%I #32 Apr 07 2017 13:48:26
%S 1,4,16,72,364,1916,10581,59681,343903,2010089
%N 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.]
%C 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.
%H Jocelyn Quaintance, <a href="http://arxiv.org/abs/math/0412244">Letter Representations of m x n x p Proper Arrays</a> (2004), arXiv:math/0412244. See Table 1.
%H Jocelyn Quaintance, <a href="http://dx.doi.org/10.1016/j.disc.2006.09.041">Combinatoric Enumeration of Two-Dimensional Proper Arrays</a>, Discrete Math., 307 (2007), 1844-1864. See Table 1.
%F See Quaintance reference for generating functions that produce A129872-A129886.
%o (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)));}
%o 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)));}
%o 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, ", "););}
%o \\ _Michel Marcus_, Mar 30 2013
%Y Cf. A129873-A129886.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, May 26 2007
%E Edited by _N. J. A. Sloane_, Nov 29 2016
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