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 A254028 #29 Mar 27 2025 14:32:57
%S A254028 6,10,20,46,116,310,860,2446,7076,20710,61100,181246,539636,1610710,
%T A254028 4815740,14414446,43177796,129402310,387944780,1163310046,3488881556,
%U A254028 10464547510,31389448220,94159956046,282463090916,847355718310
%N A254028 a(n) = 2^(n+1) + 3^n + 3.
%C A254028 This is the sequence of third terms of "second partial sums of m-th powers".
%H A254028 Colin Barker, <a href="/A254028/b254028.txt">Table of n, a(n) for n = 0..1000</a>
%H A254028 Luciano Ancora, <a href="/A254028/a254028_2.pdf">Demonstration of formulas</a>
%H A254028 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A254028 G.f.: -2*(13*x^2-13*x+3) / ((x-1)*(2*x-1)*(3*x-1)). - _Colin Barker_, Jan 24 2015
%F A254028 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - _Colin Barker_, Jan 24 2015
%F A254028 a(n) = A085279(n+1) = 2*( A099754(n)+1 ) = 2*( A094374(n)-2 ). [_Bruno Berselli_, Jan 26 2015]
%t A254028 Table[2^(n+1)+3^n+3,{n,0,30}] (* or *) LinearRecurrence[{6,-11,6},{6,10,20},30] (* _Harvey P. Dale_, Mar 27 2025 *)
%o A254028 (PARI) a(n)=2<<n + 3^n + 3 \\ _Charles R Greathouse IV_, Jan 23 2015
%o A254028 (PARI) Vec(-2*(13*x^2-13*x+3)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 24 2015
%Y A254028 Cf. A085279, A094374, A099754.
%K A254028 nonn,easy
%O A254028 0,1
%A A254028 _Luciano Ancora_, Jan 22 2015