A227299 Number of vertices for which there is an alien in-magic directed star

6, 10, 14, 15, 18, 21, 28, 33, 36, 39, 45, 55, 60, 66, 68, 78, 91, 95, 105, 120, 136, 138, 150, 153, 171, 189, 190, 203, 210, 231, 248, 253, 264, 276, 300, 315, 325, 333, 351, 378, 390, 406, 410, 435, 465, 473, 495, 496, 528, 561, 564, 588, 595, 630, 663, 666, 689, 703, 741, 770, 780, 798, 820, 861, 885

Offset

1,1

Comments

Numbers v such that there is an e in (v+1,2v-2) with s=(v+e)(v+e+1)/2v being an integer and c ceiling((2(v+e)-s)/2)=v-1.

This implies there exist an in-magic labeling of a directed star (K_{1,v-1}) containing two or more doubled edges (where a doubled edge is one in which there are two edges between a pair of vertices but the orientations of the two edges are distinct).

A graph with v vertices and e edges has an in-magic labeling if we label both the vertices and integers with the numbers 1, 2, ..., v+e using each number exactly once so that at any vertex, the sum of the vertex plus the sum of the labels on the incoming edges equals the same value for each vertex in the graph.

The first condition in our result is equivalent to sequence A024619. Thus, this is a subsequence of A024619. (Note: There are two such e for v=105).

Links

Table of n, a(n) for n=1..65.

Crossrefs

Sequence in context: A231877 A080364 A325230 * A082092 A069116 A359870

Adjacent sequences: A227296 A227297 A227298 * A227300 A227301 A227302

Keyword

nonn

Author

Alison Marr, Jul 11 2013

Status

approved