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A307203
Coordination sequence for trivalent node of type alpha'' in the first Moore pentagonal tiling.
7
1, 3, 7, 10, 14, 21, 26, 32, 38, 46, 51, 56, 61, 71, 73, 78, 84, 94, 95, 100, 107, 117, 117, 122, 130, 140, 139, 144, 153, 163, 161, 166, 176, 186, 183, 188, 199, 209, 205, 210, 222, 232, 227, 232, 245, 255, 249, 254, 268, 278, 271, 276, 291, 301, 293, 298
OFFSET
0,2
COMMENTS
There are six orbits on nodes, and six distinct coordination sequences, which are A307201 (nodes of type alpha), A307202 (alpha'), A307203 (alpha''), A307270 (alpha'''), A307204 (alpha''''), and A307206 (beta).
The group is p3m1. - Davide M. Proserpio, Apr 01 2019
REFERENCES
Herbert C. Moore, U.S. Patent 928,320, Patented July 20 1909.
LINKS
Davide M. Proserpio, Another drawing of the first Moore tiling {Labels: V1 = alpha'''', V2 = alpha''', V3 = alpha'', V4 = beta, V5 = alpha', V6 = alpha]
N. J. A. Sloane, The first Moore tiling [Constructed by copy-and-paste from the illustration in the patent]
N. J. A. Sloane, Fundamental cell
FORMULA
For n >= 10, a(n+4) = a(n) + [23,23,22,22] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019
Conjectures from Colin Barker, Apr 03 2019: (Start)
G.f.: (1 + 2*x + 5*x^2 + 5*x^3 + 7*x^4 + 8*x^5 + 4*x^6 + 8*x^7 + 3*x^8 + 4*x^9 + 2*x^10 - x^12 + x^13 - 4*x^14 + 2*x^15 - 2*x^16) / ((1 - x)^2*(1 + x)*(1 + x^2)^2).
a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4) - a(n-5) + a(n-6) - a(n-7) for n>16.
(End)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 30 2019
EXTENSIONS
Terms a(7)-a(20) from Davide M. Proserpio using ToposPro, Apr 01 2019
More terms from Rémy Sigrist, Apr 02 2019
STATUS
approved