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Search: id:A000150
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| A000150 |
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Number of dissections of an n-gon, rooted at an exterior edge, asymmetric with respect to that edge.
(Formerly M1753 N0696)
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+0
6
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| 0, 0, 1, 2, 7, 20, 66, 212, 715, 2424, 8398, 29372, 104006, 371384, 1337220, 4847208, 17678835, 64821680, 238819350, 883629164, 3282060210, 12233125112, 45741281820, 171529777432, 644952073662, 2430973096720, 9183676536076
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Number of Dyck paths of length 2n having an odd number of peaks at even height. Example: a(3)=2 because we have UDU(UD)D and U(UD)DUD, where U=(1,1), D=(1,-1) and the peaks at even height are shown between parentheses. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 13 2004
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REFERENCES
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S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751
R. K. Guy, ``Dissecting a polygon into triangles,'' Bull. Malayan Math. Soc., Vol. 5, pp. 57-60, 1958.
F. Harary and E. M. Palmer, On acyclic simplicial complexes. Mathematika 15 1968 115-122.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 78, (3.5.26).
P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Index entries for sequences related to Lyndon words
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FORMULA
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Let c(x) = (1-sqrt(1-4*x))/(2*x) = g.f. for Catalans (A000108), let d(x) = 1+x*c(x^2). Then g.f. is (c(x)-d(x))/2.
G.f.=[sqrt(1-4z^2)-sqrt(1-4z)-2z]/(4z). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 13 2004
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CROSSREFS
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a(n) = T(2n+2, n), array T as in A051168, a count of Lyndon words.
Cf. A051168, A005430.
Cf. A007595.
Sequence in context: A035071 A055891 A122877 this_sequence A115117 A029890 A095268
Adjacent sequences: A000147 A000148 A000149 this_sequence A000151 A000152 A000153
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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Additional comments from Clark Kimberling (ck6(AT)evansville.edu)
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