|
| |
|
|
A005213
|
|
Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1).
(Formerly M2254)
|
|
2
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| 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.
|
|
|
REFERENCES
| Phil Hanlon, Counting interval graphs. Trans. Amer. Math. Soc. 272 (1982), no. 2, 383-426.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
FORMULA
| 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).
|
|
|
MAPLE
| 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);
|
|
|
CROSSREFS
| Cf. A002426, A005717.
Sequence in context: A056481 A082824 A088657 * A075701 A016603 A199183
Adjacent sequences: A005210 A005211 A005212 * A005214 A005215 A005216
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 21 2003
|
| |
|
|
