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%I #25 Sep 08 2022 08:45:15
%S 1,8,29,72,145,256,413,624,897,1240,1661,2168,2769,3472,4285,5216,
%T 6273,7464,8797,10280,11921,13728,15709,17872,20225,22776,25533,28504,
%U 31697,35120,38781,42688,46849,51272,55965,60936,66193,71744,77597,83760,90241,97048,104189
%N Structured hexagonal diamond numbers (vertex structure 5).
%C Row 1 of the convolution array A213838. [_Clark Kimberling_, Jul 05 2012]
%H Vincenzo Librandi, <a href="/A100178/b100178.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (1/6)*(8*n^3-6*n^2+4*n).
%F G.f.: x*(1+4*x+3*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - _Colin Barker_, Jan 04 2012
%o (Magma) [(1/6)*(8*n^3-6*n^2+4*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 03 2011
%Y Cf. A000578 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.
%K nonn,easy
%O 1,2
%A James A. Record (james.record(AT)gmail.com), Nov 07 2004
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