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 A249127 #41 Feb 16 2025 08:33:24
%S A249127 0,1,6,12,24,35,54,70,96,117,150,176,216,247,294,330,384,425,486,532,
%T A249127 600,651,726,782,864,925,1014,1080,1176,1247,1350,1426,1536,1617,1734,
%U A249127 1820,1944,2035,2166,2262,2400,2501,2646,2752,2904,3015,3174,3290,3456,3577,3750,3876,4056,4187,4374,4510
%N A249127 a(n) = n * floor(3*n/2).
%C A249127 Union of A033570, that is (2*n+1)*(3*n+1), and A033581, that is 6*n^2.
%H A249127 Vincenzo Librandi, <a href="/A249127/b249127.txt">Table of n, a(n) for n = 0..1000</a>
%H A249127 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%H A249127 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pentagonal_number">Pentagonal number</a>
%H A249127 Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic Solid</a>
%H A249127 Wolfram MathWorld, <a href="https://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>
%H A249127 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A249127 a(n) = n * floor(3n/2) = n * A032766(n).
%F A249127 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - _Colin Barker_, Oct 22 2014
%F A249127 G.f.: -x*(2*x^3+4*x^2+5*x+1) / ((x-1)^3*(x+1)^2). - _Colin Barker_, Oct 22 2014
%F A249127 a(n) = 3/2 * n^2 + ((-1)^n-1) * n/4. E.g.f.: ((3/2)*x^2+(5/4)*x)*exp(x)-(x/4)*exp(-x). - _Robert Israel_, Oct 26 2014
%e A249127 For n=5, a(n) = 5*floor(15/2) = 5*7 = 35.
%p A249127 seq(n*floor(3*n/2), n=0..100); # _Robert Israel_, Oct 26 2014
%t A249127 Table[n Floor[3 n/2], {n, 0, 100}] (* _Vincenzo Librandi_, Oct 22 2014 *)
%o A249127 (Python)
%o A249127 from math import *
%o A249127 {print(int(n*floor(3*n/2)),end=', ') for n in range(101)}
%o A249127 (PARI) a(n)=3*n\2*n \\ _Charles R Greathouse IV_, Oct 21 2014
%o A249127 (Magma) [n*Floor(3*n/2): n in [0..60]]; // _Vincenzo Librandi_, Oct 22 2014
%o A249127 (PARI) concat(0, Vec(-x*(2*x^3+4*x^2+5*x+1)/((x-1)^3*(x+1)^2) + O(x^100))) \\ _Colin Barker_, Oct 22 2014
%Y A249127 Cf. A032766, A033581 (6*n^2), A033570 (2*n+1)*(3*n+1), A001318 (n*(3*n-1)/2).
%K A249127 nonn,easy
%O A249127 0,3
%A A249127 _Karl V. Keller, Jr._, Oct 21 2014