A086441 - OEIS

A086441

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

1, 1, 2, 4, 11, 27, 79, 213, 644, 1840, 5660 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,3`
	COMMENTS	`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.`
	LINKS	`Table of n, a(n) for n=1..11.` `Index entries for sequences obtained by enumerating foldings`
	EXAMPLE	`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.` `-- X` `/ \ /` `-----------------` `/ \ /` `/ --` `/` `oo` `---` `/ \` `/ X \` `/ \| \` `-----------------` `/ \| /` `/ .---` `/` `oo`
	CROSSREFS	`Isomorphism classes (using too generous a definition of isomorphism) from A000682. Cf. A000560, A001011.` `Sequence in context: A071314 A309886 A123441 * A316696 A319616 A148130` `Adjacent sequences: A086438 A086439 A086440 * A086442 A086443 A086444`
	KEYWORD	`nonn,more`
	AUTHOR	`N. J. A. Sloane, Sep 09 2003`
	STATUS	`approved`

Last modified February 8 23:03 EST 2023. Contains 360153 sequences. (Running on oeis4.)