This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A167471 #21 Sep 03 2025 19:46:39
%S A167471 16,128,464,1152,2320,4096,6608,9984,14352,19840,26576,34688,44304,
%T A167471 55552,68560,83456,100368,119424,140752,164480,190736,219648,251344,
%U A167471 285952,323600,364416,408528,456064,507152,561920,620496,683008,749584,820352,895440,974976
%N A167471 Janet periodic table of the elements and structured hexagonal diamond numbers. a(n) = A166911(2*n) + A166911(2*n+1).
%H A167471 Vincenzo Librandi, <a href="/A167471/b167471.txt">Table of n, a(n) for n = 1..10000</a>
%H A167471 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A167471 a(n) = 16*n*(2 - 3*n + 4*n^2)/3 = 16*A100178(n).
%F A167471 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(1)=16, a(2)=128, a(3)=464, a(4)=1152.
%F A167471 From _Elmo R. Oliveira_, Aug 28 2025: (Start)
%F A167471 G.f.: 16*x*(1 + 4*x + 3*x^2)/(1 - x)^4.
%F A167471 E.g.f.: 16*x*(3 + 9*x + 4*x^2)*exp(x)/3.
%F A167471 a(n) = A019558(n)/3. (End)
%t A167471 Table[16*n*(2 - 3*n + 4*n^2)/3, {n,1,50}] (* _G. C. Greubel_, Jun 13 2016 *)
%o A167471 (Magma) [16*n*(2-3*n+4*n^2)/3: n in [1..40]]; // _Vincenzo Librandi_, Aug 03 2011
%Y A167471 Cf. A019558, A100178, A166464, A166911.
%K A167471 nonn,easy,changed
%O A167471 1,1
%A A167471 _Paul Curtz_, Nov 04 2009