A307202 - OEIS

%I #27 Sep 07 2022 07:38:37

%S 1,3,9,15,21,24,30,42,42,45,51,69,63,66,72,96,84,87,93,123,105,108,

%T 114,150,126,129,135,177,147,150,156,204,168,171,177,231,189,192,198,

%U 258,210,213,219,285,231,234,240,312,252,255,261,339,273,276,282,366

%N Coordination sequence for trivalent node of type alpha' in the first Moore pentagonal tiling.

%C 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).

%C The group is p3m1. - _Davide M. Proserpio_, Apr 01 2019

%D Herbert C. Moore, U.S. Patent 928,320, Patented July 20 1909.

%H Rémy Sigrist, <a href="/A307202/b307202.txt">Table of n, a(n) for n = 0..1000</a>

%H Davide M. Proserpio, <a href="/A307201/a307201_1.png">Another drawing of the first Moore tiling</a> {Labels: V1 = alpha'''', V2 = alpha''', V3 = alpha'', V4 = beta, V5 = alpha', V6 = alpha]

%H Rémy Sigrist, <a href="/A307202/a307202.png">Illustration of first terms</a>

%H Rémy Sigrist, <a href="/A307202/a307202.gp.txt">PARI program for A307202</a>

%H N. J. A. Sloane, <a href="/A307201/a307201.png">The first Moore tiling</a> [Constructed by copy-and-paste from the illustration in the patent]

%H N. J. A. Sloane, <a href="/A307201/a307201_2.png">Fundamental cell</a>

%F For n >= 1, a(n+4) = a(n) + [21,21,21,27] according as n == [0,1,2,3] mod 4. - Chaim Goodman-Strauss, Mar 31 2019

%F From _Colin Barker_, Apr 03 2019: (Start)

%F G.f.: (1 + 3*x + 9*x^2 + 15*x^3 + 19*x^4 + 18*x^5 + 12*x^6 + 12*x^7 + x^8) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).

%F a(n) = 2*a(n-4) - a(n-8) for n>8. (End)

%F E.g.f.: (4 - 3*(x - 1)*cos(x) + 3*(8*x - 1)*cosh(x) + 6*sin(x) + 3*(7*x - 5)*sinh(x))/4. _Stefano Spezia_, Sep 07 2022

%o (PARI) See Links section.

%Y Cf. A307201-A307205, A307270, A307271-A307276.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 30 2019

%E Terms a(7)-a(20) from _Davide M. Proserpio_ using ToposPro, Apr 01 2019

%E More terms from _Rémy Sigrist_, Apr 02 2019