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A100010 a(0) = 2 and a(n) = f(a(n-1)) where f(n) = n^2*(3*n^2-4*n+2).

%I A100010 #29 Aug 30 2024 10:19:11
%S A100010 2,24,941184,2354066797535483525627904
%N A100010 a(0) = 2 and a(n) = f(a(n-1)) where f(n) = n^2*(3*n^2-4*n+2).
%C A100010 Previous name was: Iterated hyperdiamond numbers, starting with 24-cell(2) = 24. Hyperdiamond numbers, figurate numbers based on the 4-dimensional 24-cell, have the formula 24-cell(n) = n^2*(3*n^2-4*n+2). This sequence is the hyperdiamond number of the hyperdiamond number of ... of 2.
%C A100010 The next term has 98 digits.
%C A100010 This need not start at 24-cell(2) = 24. For example, starting at a(0) = 3, which is not a hyperdiamond number, we have a(1) = 24-cell(3) = 3^2*((3*3^2)-(4*3)+2) = 153; and a(2) = 24-cell(24-cell(3)) = 24-cell(153) = 153^2*((3*153^2)-(4*153)+2) = 1629664353; and a(3) = 24-cell(24-cell(24-cell(3))) = 24-cell(1629664353) = 21159914972910583843562449776792301953.
%D A100010 H. S. M. Coxeter, Regular Polytopes, 3rd ed. New York: Dover, 1973.
%H A100010 Michel Marcus, <a href="/A100010/b100010.txt">Table of n, a(n) for n = 0..5</a>
%H A100010 Hyun Kwang Kim, <a href="http://dx.doi.org/10.1090/S0002-9939-02-06710-2">On Regular Polytope Numbers</a>, Proc. Amer. Math. Soc., 131 (2003), 65-75.
%H A100010 Jonathan Vos Post, <a href="https://web.archive.org/web/20100701204436/http://magicdragon.com/poly.html">Table of Polytope Numbers, Sorted, Through 1,000,000</a>.
%F A100010 a(0) = 2; hyperdiamond numbers, figurate numbers based on the 4-dimensional 24-cell, have the formula 24-cell(n) = n^2*(3*n^2-4*n+2). a(1) = 24-cell(2) = 24. a(2) = 24-cell(24-cell(2)) = 941184. For k>1, a(k+1) = 24-cell(a(k)).
%e A100010 a(0) = 2 is the seed for this instance of the more general recurrence;
%e A100010 a(1) = 24-cell(2) = 2^2*(3*2^2-4*2+2) = 24;
%e A100010 a(2) = 24-cell(24-cell(2)) = 24-cell(24) = 24^2*(3*24^2-4*24+2) = 941184.
%o A100010 (PARI) f(n) = n^2*(3*n^2-4*n+2); \\ A092181
%o A100010 a(n) = if (n==0, 2, f(a(n-1))); \\ _Michel Marcus_, Dec 14 2015
%Y A100010 Cf. A092181, A007501, A099179, A000332.
%K A100010 easy,nonn
%O A100010 0,1
%A A100010 _Jonathan Vos Post_, Nov 16 2004
%E A100010 New name from _Joerg Arndt_, Feb 23 2022