A038151 Bilateral directed animals in first and 8th octants.

1, 1, 3, 8, 23, 67, 198, 590, 1769, 5328, 16103, 48801, 148216, 450952, 1374044, 4191814, 12801243, 39127766, 119687036, 366348367, 1121992447, 3437981365, 10539237135, 32321011234, 99154404456, 304280556111, 934022848612

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.

Links

Table of n, a(n) for n=1..27.

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

Sequence in context: A106606 A050535 A025578 * A230122 A199103 A057198

Adjacent sequences: A038148 A038149 A038150 * A038152 A038153 A038154

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