Search: id:A092181
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%I A092181
%S A092181 1,24,153,544,1425,3096,5929,10368,16929,26200,38841,55584,77233,104664,
%T A092181 138825,180736,231489,292248,364249,448800,547281,661144,791913,941184,
%U A092181 1110625,1301976,1517049,1757728,2025969,2323800,2653321,3016704
%N A092181 Figurate numbers based on the 24-cell (4-D polytope with Schlaefli symbol 
               {3,4,3}).
%C A092181 This is the 4-dimensional regular convex polytope called the 24-cell, 
               hyperdiamond or icositetrachoron.
%H A092181 Hyun Kwang Kim, <a href="http://com2mac.postech.ac.kr/papers/2001/01-22.pdf">
               On Regular Polytope Numbers</a>.
%H A092181 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               24-Cell.html">24-Cell</a>
%F A092181 a(n)=n^2*((3*n^2)-(4*n)+2)
%F A092181 a(n) = C(n+3,4) + 19 C(n+2,4) + 43 C(n+1,4) + 9 C(n,4)
%e A092181 a(3)= 3^2*((3*3^2)-(4*3)+2) = 9*(27-12+2) = 9*17 = 153
%Y A092181 Cf. A000332, A000583, A014820, A092182, A092183.
%Y A092181 Sequence in context: A042118 A039494 A159650 this_sequence A001702 A004308 
               A008663
%Y A092181 Adjacent sequences: A092178 A092179 A092180 this_sequence A092182 A092183 
               A092184
%K A092181 easy,nonn
%O A092181 1,2
%A A092181 Michael J. Welch (mjw1(AT)ntlworld.com), Mar 31 2004

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