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%I #22 Sep 08 2022 08:45:15
%S 1,32,147,400,845,1536,2527,3872,5625,7840,10571,13872,17797,22400,
%T 27735,33856,40817,48672,57475,67280,78141,90112,103247,117600,133225,
%U 150176,168507,188272,209525,232320,256711,282752
%N Structured rhombic triacontahedral numbers (vertex structure 7).
%C Also structured pentakis dodecahedral numbers (vertex structure 7) (cf. A100173 = alternate vertex).
%H Vincenzo Librandi, <a href="/A100165/b100165.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/6)*(54*n^3 - 72*n^2 + 24*n) = n*(3*n-2)^2.
%F From _Jaume Oliver Lafont_, Sep 08 2009: (Start)
%F a(n) = (3*(n-1) + 1)^2*(3*(n-1) + 3)/3.
%F G.f.: x*(1 + 28*x + 25*x^2)/(1-x)^4. (End)
%t Table[(3(n-1)+1)^2(3(n-1)+3)/3,{n,40}] (* _Harvey P. Dale_, Jan 02 2020 *)
%o (Magma) [(1/6)*(54*n^3-72*n^2+24*n): n in [1..40]]; // _Vincenzo Librandi_, Jul 26 2011
%Y Cf. A100164 = alternate vertex; A100145 for more on structured numbers.
%Y Cf. A260260 (comment). [_Bruno Berselli_, Jul 22 2015]
%K nonn,easy
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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