%I A100145
%S A100145 1,120,579,1600,3405,6216,10255,15744,22905,31960,43131,56640,72709,
%T A100145 91560,113415,138496,167025,199224,235315,275520,320061,369160,423039,
%U A100145 481920,546025,615576,690795,771904,859125,952680,1052791,1159680
%N A100145 Structured great rhombicosidodecahedral numbers.
%C A100145 Structured polyhedral numbers are a type of figurate polyhedral numbers. 
               Structurate polyhedra differ from regular figurate polyhedra by having 
               appropriate figurate polygonal faces at any iteration, i.e. a regular 
               truncated octahedron, n=2, would have 7 points on its hexagonal faces, 
               whereas a structured truncated octahedron, n=2, would have 6 points 
               - just as a hexagon, n=2, would have. Like regular figurate polygons, 
               structured polyhedra seem to originate at a vertex and since many 
               polyhedra have different vertices (a pentagonal diamond has 2 "polar" 
               vertices with 5 adjacent vertices and 5 "equatorial" vertices with 
               4 adjacent vertices), these polyhedra have multiple structured number 
               sequences, dependent on the "vertex structures" which are each equal 
               to the one vertex itself plus its adjacent vertices. For polystructurate 
               polyhedra the notation, structured polyhedra (vertex structure x) 
               is used to differentiate between alternate vertices, where VS stands 
               for vertex structure.
%F A100145 a(n)=(1/6)*(222*n^3-312*n^2+96*n)
%F A100145 Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 
               08 2009: (Start)
%F A100145 a(n)=(1+(n-1))*(1+22*(n-1)+37*(n-1)^2)
%F A100145 G.f.: x*(1+116*x+105*x^2)/(1-x)^4 (End)
%Y A100145 Cf. A051673, A100146 through A100156 - structured Archimedean solids; 
               A100157 through A100175 - structured Catalan solids; A100147 - structured 
               prisms; A000447 - structured diamonds; A100185 - structured anti-prisms; 
               and A100188 - structured anti-diamonds.
%Y A100145 Sequence in context: A067915 A115619 A152622 this_sequence A090216 A113546 
               A166069
%Y A100145 Adjacent sequences: A100142 A100143 A100144 this_sequence A100146 A100147 
               A100148
%K A100145 easy,nonn
%O A100145 1,2
%A A100145 James A. Record (james.record(AT)gmail.com), Nov 07, 2004.
%E A100145 Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006