login
Number of vertices of Goldberg-Casper-Klug pseudo-icosahedra.
2

%I #17 Jun 17 2020 17:16:29

%S 12,32,42,72,92,122,132,162,192,212,252,272,282,312,362,372,392,432,

%T 482,492,522,572,612,632,642,672,732,752,762,792,812,842,912,932,972,

%U 1002,1032,1082,1092,1112,1122,1172,1212,1242,1272,1292,1332,1392,1442,1472

%N Number of vertices of Goldberg-Casper-Klug pseudo-icosahedra.

%C Refers to the capsomere count in virus architectural structures. Since the Loeschian numbers (A003136) of the form x^2 + xy + y^2 reduce to squares (A000290) when either x or y equals 0, a(n) contains A005901 which is 10*n^2 + 2.

%D I. Stewart, "Game, Set and Math", Chapter 6, Table 6.1 pp. 81 Penguin London 1991.

%H Michael De Vlieger, <a href="/A071336/b071336.txt">Table of n, a(n) for n = 1..1200</a>

%H K. Urner, <a href="http://www.4dsolutions.net/synergetica/synergetica2.html">Synergetica:A case of Deja Vu</a>

%F a(n) = 10*A003136(n+1) + 2. [corrected by _Georg Fischer_, Jun 17 2020]

%t 10 # + 2 & /@ Rest@ Flatten[Position[CoefficientList[QPochhammer[q]^3/QPochhammer[q^3]/3 + O[q]^150, q], n_ /; n != 0] - 1] (* _Michael De Vlieger_, Jun 17 2020, after _Jean-François Alcover_ at A003136 *)

%Y Cf. A003136, A005901.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Oct 30 2003