OFFSET
0,2
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..5000
Michel Deza and Mikhail Shtogrin, Isometric embedding of mosaics into cubic lattices, Discrete mathematics 244.1-3 (2002): 43-53. See Fig. 2.
Michel Deza and Mikhail Shtogrin, Isometric embedding of mosaics into cubic lattices, Discrete mathematics 244.1-3 (2002): 43-53. [Annotated scan of page 52 only]
Rémy Sigrist, PARI program for A316317
Rémy Sigrist, Illustration of first terms
N. J. A. Sloane, Initial terms of coordination sequence for trivalent node
FORMULA
Apparently, a(n + 12) = a(n) + 40 for any n > 0. - Rémy Sigrist, Jun 30 2018
This can surely be proved by the Coloring Book Method, although I have not worked out the details. See A316316 for the corresponding proof for a tetravalent node. - N. J. A. Sloane, Jun 30 2018
G.f. (assuming above conjecture): (1+x)^2*(1+3*x^2+x^4)/((1-x)^2*(1+x+x^2)*(1+x^2)). - Robert Israel, Jul 01 2018
a(n) = (30*n - 9*A056594(n-1) + 6*A102283(n))/9 for n > 0. - Conjectured by Stefano Spezia, Jun 12 2021
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 29 2018
EXTENSIONS
More terms from Rémy Sigrist, Jun 30 2018
STATUS
approved