cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086441 Number of inequivalent ways a semi-infinite curve can cross a straight line n times.

This page as a plain text file.
%I A086441 #9 Apr 16 2021 00:13:51
%S A086441 1,1,2,4,11,27,79,213,644,1840,5660
%N A086441 Number of inequivalent ways a semi-infinite curve can cross a straight line n times.
%C A086441 This uses a too broad notion of equivalence. Besides the obvious reflection in a plane perpendicular to the straight line, if the end of the curve is in a free region of the plane, it is extended to infinity and the direction of the curve can then be reversed. A000560 uses a better definition of equivalence.
%H A086441 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%e A086441 The a(3) = 2 solutions with 3 crossings. The line is drawn horizontally. The curve starts at oo and ends at X. The crossings are indicated by stars.
%e A086441        --        X
%e A086441       /  \      /
%e A086441 -----*----*----*----
%e A086441     /      \  /
%e A086441    /        --
%e A086441   /
%e A086441 oo
%e A086441          ---
%e A086441         /   \
%e A086441        /  X  \
%e A086441       /   |   \
%e A086441 -----*----*----*----
%e A086441     /     |   /
%e A086441    /      .---
%e A086441   /
%e A086441 oo
%Y A086441 Isomorphism classes (using too generous a definition of isomorphism) from A000682. Cf. A000560, A001011.
%K A086441 nonn,more
%O A086441 1,3
%A A086441 _N. J. A. Sloane_, Sep 09 2003