A343296 - OEIS

A343296

a(n) is the number of graceful graphs with n edges and round(sqrt(3n+9/4)) vertices.

1, 2, 1, 8, 4, 1, 44, 16, 4, 482, 216, 52, 12, 5604, 1890, 432, 84, 130712, 49440, 12132, 3016, 452, 64, 874522, 238464, 48904, 9304, 960, 320, 11115400, 2750276, 510944, 104968, 7752, 2688, 384, 86095888, 17626256, 3666896, 561216, 113664, 5760, 1536, 1689874496, 408492760, 71673808, 13136640, 2118528, 381696, 21504

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OFFSET

1,2

COMMENTS

Next term a(51)=0 if excess values A326499 are not allowed.

These are the numbers of graceful graphs with n edges and minimal vertices, up to a(50).

a(51) = 101666311328 is in this alternative sequence.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

Sparse rulers (0,1,4,7,9) and (0,1,2,6,9) can each make 2 graceful graphs so a(9)=4.

CROSSREFS