OFFSET
1,3
COMMENTS
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.
The Motzkin transform of (A000931 without first 2 terms). [From R. J. Mathar, Dec 11 2008]
REFERENCES
Stanley, R. P., Enumerative Combinatorics, Volume 2, Cambridge University Press, 1999. Problem 6.19 (kkk),6.34
Shapiro, L., From Directed Animals to Motzkin Paths, Preprint.
FORMULA
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.]
(-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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seyoum Getu (getu(AT)scs.howard.edu)
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
STATUS
approved