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 A100175 #28 Mar 18 2023 08:39:41
%S A100175 1,8,30,76,155,276,448,680,981,1360,1826,2388,3055,3836,4740,5776,
%T A100175 6953,8280,9766,11420,13251,15268,17480,19896,22525,25376,28458,31780,
%U A100175 35351,39180,43276,47648,52305,57256,62510,68076,73963,80180,86736,93640,100901,108528
%N A100175 Structured triakis tetrahedral numbers (vertex structure 4).
%C A100175 Equals binomial transform of [1, 7, 15, 9, 0, 0, 0, ...] where (1, 7, 15, 9) = row 3 of triangle A038763. - _Gary W. Adamson_, Jul 19 2008
%C A100175 Equals convolution square of 1, 4, 7, 10, 13, 16, 19, ..., A016777. - _Gary W. Adamson_, Jul 28 2009
%H A100175 Vincenzo Librandi, <a href="/A100175/b100175.txt">Table of n, a(n) for n = 1..10000</a>
%H A100175 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A100175 a(n) = (3*n^3 - 3*n^2 + 2*n)/2.
%F A100175 G.f.: x*(2*x+1)^2 / ( (x-1)^4 ).
%t A100175 CoefficientList[Series[x (2x+1)^2/((x-1)^4),{x,0,50}],x] (* or *) LinearRecurrence[{4,-6,4,-1},{0,1,8,30},50] (* _Harvey P. Dale_, Mar 18 2023 *)
%o A100175 (Magma) [(3*n^3-3*n^2+2*n)/2: n in [1..50] ]; // _Vincenzo Librandi_, Aug 02 2011
%Y A100175 Cf. A000578 (alternate vertex), A100145 for more on structured numbers.
%Y A100175 Cf. A038763.
%K A100175 easy,nonn
%O A100175 1,2
%A A100175 James A. Record (james.record(AT)gmail.com), Nov 07 2004