Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A000912
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A000912 Expansion of (sqrt(1-4x^2)-sqrt(1-4x))/(2x). +0
2
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; listen)
OFFSET

0,3

COMMENT

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

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)=binom(2n, n)/(n+1) are the Catalan numbers (A000108). a(n)=2*A000150(n) for n>0. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 (pbarry(AT)wit.ie), Apr 11 2007

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); (Deutsch)

CROSSREFS

Sequence in context: A006252 A079995 A152011 this_sequence A128750 A047152 A007866

Adjacent sequences: A000909 A000910 A000911 this_sequence A000913 A000914 A000915

KEYWORD

nonn

AUTHOR

E. K. Lloyd (E.K.Lloyd(AT)soton.ac.uk)

EXTENSIONS

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2004

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


AT&T Labs Research