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%I #11 Jul 23 2017 12:34:28
%S 1,1,3,8,23,67,198,590,1769,5328,16103,48801,148216,450952,1374044,
%T 4191814,12801243,39127766,119687036,366348367,1121992447,3437981365,
%U 10539237135,32321011234,99154404456,304280556111,934022848612
%N Bilateral directed animals in first and 8th octants.
%C The sequence counts subsets S of N X N with n elements such that if (i,j) is in S, then i >= absolute value of j and there is a lattice path from (0,0) to (i,j) with steps (0,1), (1,0) and (0,-1) lying entirely inside S.
%C The Motzkin transform of (A000931 without first 2 terms). [From _R. J. Mathar_, Dec 11 2008]
%D Stanley, R. P., Enumerative Combinatorics, Volume 2, Cambridge University Press, 1999. Problem 6.19 (kkk),6.34
%D Shapiro, L., From Directed Animals to Motzkin Paths, Preprint.
%F G.f.: x/(1-x*(1+x)*m), where m = (1 - x - (1-2*x-3*x^2)^(1/2))/(2*x^2) is the generating function for the Motzkin numbers (A001006). [Corrected by _N. J. A. Sloane_, Sep 22 2010, at the suggestion of _Vladimir Kruchinin_.
%F (-n+1)*a(n) +2*(2*n-3)*a(n-1) +2*(n-5)*a(n-2) +(-11*n+41)*a(n-3) +(-11*n+49)*a(n-4) +3*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Jul 23 2017
%K nonn,easy
%O 1,3
%A Seyoum Getu (getu(AT)scs.howard.edu)
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
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