A071336 Number of vertices of Goldberg-Casper-Klug pseudo-icosahedra.

12, 32, 42, 72, 92, 122, 132, 162, 192, 212, 252, 272, 282, 312, 362, 372, 392, 432, 482, 492, 522, 572, 612, 632, 642, 672, 732, 752, 762, 792, 812, 842, 912, 932, 972, 1002, 1032, 1082, 1092, 1112, 1122, 1172, 1212, 1242, 1272, 1292, 1332, 1392, 1442, 1472

Offset: 1

Author

Lekraj Beedassy, Oct 30 2003

Keywords

• nonn

Comments

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.

References

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1200
• K. Urner, Synergetica:A case of Deja Vu

Crossrefs

Cf. A003136, A005901.

Programs

Mathematica

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 *)

Formula

a(n) = 10*A003136(n+1) + 2. [corrected by Georg Fischer, Jun 17 2020]