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A316317
Coordination sequence for trivalent node in chamfered version of square grid.
4
1, 3, 6, 11, 14, 15, 20, 25, 26, 29, 34, 37, 40, 43, 46, 51, 54, 55, 60, 65, 66, 69, 74, 77, 80, 83, 86, 91, 94, 95, 100, 105, 106, 109, 114, 117, 120, 123, 126, 131, 134, 135, 140, 145, 146, 149, 154, 157, 160, 163, 166, 171, 174, 175, 180, 185, 186, 189, 194
OFFSET
0,2
LINKS
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]
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
See A316316 for tetravalent node.
See A250120 for links to thousands of other coordination sequences.
Cf. A316358 (partial sums).
Sequence in context: A316096 A310091 A136981 * A074737 A310092 A190439
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 29 2018
EXTENSIONS
More terms from Rémy Sigrist, Jun 30 2018
STATUS
approved