login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329908 Number of oriented rational links with crossing number n. 4
2, 2, 5, 6, 15, 24, 51, 90, 187, 352, 715, 1386, 2795, 5504, 11051, 21930, 43947, 87552, 175275, 349866, 700075, 1398784, 2798251, 5593770, 11188907, 22372352, 44747435, 89483946, 178973355, 357924864, 715860651, 1431677610, 2863377067, 5726666752, 11453377195 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..36.

Yuanan Diao, Michael Finney, and Dawn Ray, The number of oriented rational links with a given deficiency number, arXiv:2007.02819 [math.GT], 2020. See Theorem 3 p.9 and Table 1 p. 14.

C. Ernst and D. W. Sumners, The Growth of the Number of Prime Knots, Math. Proc. Cambridge Philos. Soc. 102, 303-315, 1987 (see Theorem 1, formulas for TL_n^*).

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,0,-2,-4).

FORMULA

a(n) = (2^(n-1)+1)/3 + 2^(n/2-1) if n is even; (2^(n-1)+2^((n-1)/2)-2)/3 if n is odd and n == 1 mod 4; (2^(n-1)+2^((n-1)/2))/3) if n is odd and n == 3 mod 4.

G.f.: x^2*(2 - 3*x^2 - 3*x^3 - 4*x^4)/(1 - x - 3*x^2 + x^3 + 2*x^5 + 4*x^6). - Jinyuan Wang, Jul 08 2020

PROG

(PARI) a(n) = if (n%2, if ((n%4)==1, (2^(n-1)+2^((n-1)/2)-2)/3, (2^(n-1)+2^((n-1)/2))/3), (2^(n-1)+1)/3 + 2^(n/2-1));

CROSSREFS

Cf. A018240, A090597, A336398.

Sequence in context: A028410 A050216 A320296 * A295198 A080880 A305606

Adjacent sequences:  A329905 A329906 A329907 * A329909 A329910 A329911

KEYWORD

nonn,easy

AUTHOR

Michel Marcus, Jul 07 2020

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)