This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005213 Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1). (Formerly M2254) 3
 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; text; 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Phil Hanlon, Counting interval graphs, Trans. Amer. Math. Soc. 272 (1982), no. 2, 383-426. FORMULA G.f.: ((1+2*z-z^2)/sqrt(1-2*z^2-3*z^4)-1)/(2*z). a(2*n) = A002426(n), a(2*n+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); MATHEMATICA CoefficientList[Series[((1 + 2*z - z^2)/Sqrt[1 - 2*z^2 - 3*z^4] - 1)/(2*z), {z, 0, 50}], z] (* G. C. Greubel, Mar 02 2017 *) PROG (PARI) x='x +O('x^50); Vec(((1+2*x-x^2)/sqrt(1-2*x^2-3*x^4)-1)/(2*x)) \\ G. C. Greubel, Mar 02 2017 CROSSREFS Cf. A002426, A005717. Sequence in context: A305123 A082824 A088657 * A075701 A016603 A199183 Adjacent sequences:  A005210 A005211 A005212 * A005214 A005215 A005216 KEYWORD nonn AUTHOR EXTENSIONS Edited by Emeric Deutsch, Nov 21 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 10:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)