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A316317 Coordination sequence for trivalent node in chamfered version of square grid. 3
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 (list; graph; refs; listen; history; text; internal format)
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

MATHEMATICA

Join[{1}, LinearRecurrence[{1, -1, 2, -1, 1, -1}, {3, 6, 11, 14, 15, 20}, 100]] (* Jean-François Alcover, Dec 13 2018 *)

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

Adjacent sequences:  A316314 A316315 A316316 * A316318 A316319 A316320

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 29 2018

EXTENSIONS

More terms from Rémy Sigrist, Jun 30 2018

STATUS

approved

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Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)