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Search: id:A038151
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| A038151 |
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Bilateral directed animals in first and 8th octants. |
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+0
1
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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 (mathar(AT)strw.leidenuniv.nl), Dec 11 2008]
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REFERENCES
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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.
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FORMULA
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G.f.: 1/(1-x(1+x)m), where m is the generating function for the Motzkin numbers.
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CROSSREFS
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Sequence in context: A106606 A050535 A025578 this_sequence A057198 A025262 A056010
Adjacent sequences: A038148 A038149 A038150 this_sequence A038152 A038153 A038154
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KEYWORD
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nonn,easy
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AUTHOR
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Seyoum Getu (getu(AT)scs.howard.edu)
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
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