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%I #14 Sep 08 2022 08:45:48
%S 16,128,464,1152,2320,4096,6608,9984,14352,19840,26576,34688,44304,
%T 55552,68560,83456,100368,119424,140752,164480,190736,219648,251344,
%U 285952,323600,364416,408528,456064,507152,561920,620496,683008,749584
%N Janet periodic table of the elements and structured hexagonal diamond numbers. a(n) = A166911(2n) + A166911(2n+1).
%C (A166911=3,13,39,89,171,293,). 5 formulas for a(n):fifth is a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4), a(0)=16,a(1)=128,a(2)=464,a(3)=1152. See A166464 and its companion A166911 (offset 0). Note, for a(n) mod 10, period 5:repeat 6,8,4,2,0. Mathematically, a(n) (then A100178=1,8,29,72,145,) can be preceded by 0.
%H Vincenzo Librandi, <a href="/A167471/b167471.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 16*n*(2-3*n+4*n^2)/3 = 16*(2*n-3*n^2+4*n^3)/3 = 16*A100178(n).
%t Table[16*n*(2 - 3*n + 4*n^2)/3, {n,1,50}] (* _G. C. Greubel_, Jun 13 2016 *)
%o (Magma) [16*n*(2-3*n+4*n^2)/3: n in [1..40]]; // _Vincenzo Librandi_, Aug 03 2011
%K nonn,easy
%O 1,1
%A _Paul Curtz_, Nov 04 2009