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Search: id:A039919
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| A039919 |
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Related to enumeration of edge-rooted catafusenes. |
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5
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| 0, 1, 5, 21, 86, 355, 1488, 6335, 27352, 119547, 528045, 2353791, 10575810, 47849685, 217824285, 996999525, 4585548680, 21182609875, 98236853415, 457211008415, 2134851575050, 9997848660345, 46949087361550
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Binomial transform of the first differences of the Catalan numbers (see A000245). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2006
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 19 2009: (Start)
Starting (1, 5, 21,...) = A002212, (1, 3, 10, 36, 137,...) convolved with
A007317, (1, 2, 5, 15, 51,...). (End)
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REFERENCES
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B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons ..., Monat. f. Chemie, 125 (1994), 1327-1337 (see Eq. 6).
S. J. Cyvin et al., Enumeration and classification of benzenoid systems. 32. Normal perifusenes with two internal vertices, J. Chem. Inform. Comput. Sci., 32 (1992), 532-540.
S. J. Cyvin et al., Enumeration and classification of certain polygonal systems... : annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
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FORMULA
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G.f.: 8x^2*(1-x)/(1-x+sqrt(1-6x+5x^2))^3. - EmericDeutsch(AT)msn.com (deutsch(AT)duke.poly.edu), Oct 24 2002
a(n)=A002212(n)-sum(A002212(j), j=0..n-1)). Example: a(5)=137-(1+1+3+10+36)=86. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 23 2004
a(n)=sum{k=0..n, C(n,k)(C(k+1)-C(k))}; - Paul Barry (pbarry(AT)wit.ie), Feb 16 2006
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CROSSREFS
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Cf. A002212.
A002212, A007317 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 19 2009]
Sequence in context: A026855 A097113 A012814 this_sequence A010925 A019992 A010917
Adjacent sequences: A039916 A039917 A039918 this_sequence A039920 A039921 A039922
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from EmericDeutsch(AT)msn.com (deutsch(AT)duke.poly.edu), Oct 24 2002
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