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Search: id:A005213
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| A005213 |
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Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1).
(Formerly M2254)
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+0
3
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| 1, 0, 1, 1, 3, 2, 7, 6, 19, 16, 51, 45, 141, 126, 393, 357, 1107, 1016, 3139, 2907, 8953, 8350, 25653, 24068, 73789, 69576, 212941, 201643, 616227, 585690, 1787607, 1704510, 5196627, 4969152, 15134931, 14508939, 44152809, 42422022, 128996853
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Also, number of symmetric Dyck paths of semilength n with no peaks at odd level. E.g. a(4)=3 because we have UUUUDDDD, UUDDUUDD and UUDUDUDD, where U=(1,1) and D=(1,-1).
Sequence is obtained by alternating A002426 and A005717.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Phil Hanlon, Counting interval graphs. Trans. Amer. Math. Soc. 272 (1982), no. 2, 383-426.
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FORMULA
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G.f.=[(1+2z-z^2)/sqrt(1-2z^2-3z^4)-1]/(2z). a(2n)=A002426(n), a(2n+1)=[A002426(n+1)-A002426(n)]/2 (A002426(n) are the central trinomial coefficients).
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MAPLE
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G:=((1+2*z-z^2)/sqrt(1-2*z^2-3*z^4)-1)/(2*z): Gser:=series(G, z=0, 40): 1, seq(coeff(Gser, z^n), n=1..38);
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CROSSREFS
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Cf. A002426, A005717.
Sequence in context: A056481 A082824 A088657 this_sequence A075701 A016603 A120633
Adjacent sequences: A005210 A005211 A005212 this_sequence A005214 A005215 A005216
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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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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 21 2003
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