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A298022 Coordination sequence for Dual(3^3.4^2) tiling with respect to a trivalent node. 22
1, 3, 7, 12, 17, 23, 28, 33, 37, 42, 47, 51, 56, 61, 65, 70, 75, 79, 84, 89, 93, 98, 103, 107, 112, 117, 121, 126, 131, 135, 140, 145, 149, 154, 159, 163, 168, 173, 177, 182, 187, 191, 196, 201, 205, 210, 215, 219, 224, 229, 233, 238, 243, 247, 252, 257, 261 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This tiling is also called the prismatic pentagonal tiling, or the cem-d net. It is one of the 11 Laves tilings.

REFERENCES

B. Gruenbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987. See p. 96.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..1000

Reticular Chemistry Structure Resource (RCSR), The cem-d tiling (or net)

Rémy Sigrist, PARI program for A298022

N. J. A. Sloane, Overview of coordination sequences of Laves tilings [Fig. 2.7.1 of Grünbaum-Shephard 1987 with A-numbers added and in some cases the name in the RCSR database]

N. J. A. Sloane, Illustration of initial terms

FORMULA

Conjectures from Colin Barker, Jan 22 2018: (Start)

G.f.: (1 + 2*x + 4*x^2 + 4*x^3 + 3*x^4 + 2*x^5 - 2*x^8) / ((1 - x)^2*(1 + x + x^2)).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.

(End)

PROG

(PARI) See Links section.

CROSSREFS

See A298023 for partial sums, A298024 for a tetravalent point.

List of coordination sequences for Laves tilings (or duals of uniform planar nets): [3,3,3,3,3.3] = A008486; [3.3.3.3.6] = A298014, A298015, A298016; [3.3.3.4.4] = A298022, A298024; [3.3.4.3.4] = A008574, A296368; [3.6.3.6] = A298026, A298028; [3.4.6.4] = A298029, A298031, A298033; [3.12.12] = A019557, A298035; [4.4.4.4] = A008574; [4.6.12] = A298036, A298038, A298040; [4.8.8] = A022144, A234275; [6.6.6] = A008458.

Sequence in context: A310246 A310247 A310248 * A227133 A170883 A198463

Adjacent sequences:  A298019 A298020 A298021 * A298023 A298024 A298025

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 21 2018

EXTENSIONS

More terms from Rémy Sigrist, Jan 21 2018

STATUS

approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)