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A038151 Bilateral directed animals in first and 8th octants. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)