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 A100178 #36 Aug 29 2025 10:16:24
%S A100178 1,8,29,72,145,256,413,624,897,1240,1661,2168,2769,3472,4285,5216,
%T A100178 6273,7464,8797,10280,11921,13728,15709,17872,20225,22776,25533,28504,
%U A100178 31697,35120,38781,42688,46849,51272,55965,60936,66193,71744,77597,83760,90241,97048,104189
%N A100178 Structured hexagonal diamond numbers (vertex structure 5).
%C A100178 Row 1 of the convolution array A213838. - _Clark Kimberling_, Jul 05 2012
%H A100178 Vincenzo Librandi, <a href="/A100178/b100178.txt">Table of n, a(n) for n = 1..10000</a>
%H A100178 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A100178 a(n) = (1/6)*(8*n^3 - 6*n^2 + 4*n).
%F A100178 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
%F A100178 From _Elmo R. Oliveira_, Aug 28 2025: (Start)
%F A100178 E.g.f.: exp(x)*x*(4*x^2 + 9*x + 3)/3.
%F A100178 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
%F A100178 a(n) = A167471(n)/16 = A019558(n)/48. (End)
%t A100178 LinearRecurrence[{4, -6, 4, -1}, {1, 8, 29, 72}, 50] (* _Paolo Xausa_, Aug 06 2025 *)
%o A100178 (Magma) [(1/6)*(8*n^3-6*n^2+4*n): n in [1..40]]; // _Vincenzo Librandi_, Aug 03 2011
%Y A100178 Cf. A000578 (alternate vertex), A000447 (structured diamonds) A100145 (for more on structured numbers).
%Y A100178 Cf. A019558, A167471, A213838.
%K A100178 nonn,easy,changed
%O A100178 1,2
%A A100178 James A. Record (james.record(AT)gmail.com), Nov 07 2004