The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000912 Expansion of (sqrt(1-4x^2) - sqrt(1-4x))/(2x). 3
 1, 0, 2, 4, 14, 40, 132, 424, 1430, 4848, 16796, 58744, 208012, 742768, 2674440, 9694416, 35357670, 129643360, 477638700, 1767258328, 6564120420, 24466250224, 91482563640, 343059554864, 1289904147324, 4861946193440, 18367353072152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of bond-rooted polyenoids with 2n-1 edges. Partial sums are A129366. REFERENCES 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 LINKS T. D. Noe, Table of n, a(n) for n = 0..200 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. [Annotated scanned copy] FORMULA a(n) = C(n) if n is even and a(n) = C(n) -C((n-1)/2) if n is odd, where C(n) = binomial(2n, n)/(n+1) are the Catalan numbers (A000108). a(n) = 2*A000150(n) for n > 0. - Emeric Deutsch, Dec 19 2004 G.f.: c(x) - x*c(x^2), where c(x) = g.f. for A000108; a(n) = C(n) - C((n-1)/2)(1-(-1)^n)/2, C(n) = A000108(n). - Paul Barry, Apr 11 2007 Conjecture: n*(n+1)*a(n) - 6*n*(n-1)*a(n-1) + 4*(2*n^2-10*n+9)*a(n-2) + 8*(n^2+n-9)*a(n-3) - 48*(n-3)*(n-4)*a(n-4) + 32*(2*n-9)*(n-5)*a(n-5) = 0. - R. J. Mathar, Nov 24 2012 MAPLE c:=n->binomial(2*n, n)/(n+1):a:=proc(n) if n mod 2 = 1 then c(n+1) else c(n+1)-c(n/2) fi end: seq(a(n), n=0..28); # Emeric Deutsch, Dec 19 2004 MATHEMATICA nn = 200; CoefficientList[Series[(Sqrt[1 - 4 x^2] - Sqrt[1 - 4 x])/(2 x), {x, 0, nn}], x] (* T. D. Noe, Jun 20 2012 *) Table[If[EvenQ[n], CatalanNumber[n], CatalanNumber[n]-CatalanNumber[(n-1)/ 2]], {n, 0, 30}] (* Harvey P. Dale, Oct 30 2013 *) CROSSREFS Sequence in context: A079995 A279322 A152011 * A228477 A169982 A243323 Adjacent sequences:  A000909 A000910 A000911 * A000913 A000914 A000915 KEYWORD nonn AUTHOR E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk) EXTENSIONS More terms from Emeric Deutsch, Dec 19 2004 Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar 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 January 20 00:34 EST 2022. Contains 350467 sequences. (Running on oeis4.)