%I #16 Sep 08 2022 08:45:15
%S 1,4,19,68,185,416,819,1464,2433,3820,5731,8284,11609,15848,21155,
%T 27696,35649,45204,56563,69940,85561,103664,124499,148328,175425,
%U 206076,240579,279244,322393,370360,423491,482144
%N Structured meta-anti-prism numbers, the n-th number from a structured n-gonal anti-prism number sequence.
%H Vincenzo Librandi, <a href="/A100185/b100185.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (1/6)*(3*n^4 - 8*n^3 + 9*n^2 + 2*n).
%F G.f.: x*(1 - x + 9*x^2 + 3*x^3)/(1-x)^5. [_Colin Barker_, Jun 08 2012]
%e There are no 1- or 2-gonal anti-prisms, so 1 and (2n) are used as the first and second terms since all the sequences begin as such.
%o (Magma) [(1/6)*(3*n^4-8*n^3+9*n^2+2*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 03 2011
%Y Cf. A005900, A000447, A096000, A100178, A100157, A100185 - structured anti-prisms; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
%K easy,nonn
%O 1,2
%A James A. Record (james.record(AT)gmail.com)