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 A254363 #21 Sep 12 2024 20:35:47
%S A254363 20,35,77,203,605,1955,6677,23723,86765,324275,1231877,4738043,
%T A254363 18396125,71940995,282882677,1116985163,4424500685,17568076115,
%U A254363 69883311077,278367837083,1109978272445,4429440153635,17686354389077,70651224045803,282322365983405,1128441973997555,4511225627508677,18037276107243323,72126226025905565
%N A254363 a(n) = 4^n + 6*2^n + 3^(n+1) + 10.
%C A254363 This is the sequence of fourth terms of "third partial sums of m-th powers".
%H A254363 Colin Barker, <a href="/A254363/b254363.txt">Table of n, a(n) for n = 0..1000</a>
%H A254363 Luciano Ancora, <a href="https://oeis.org/A254364/a254364.pdf">Demonstration of formulas</a>, page 2.
%H A254363 Luciano Ancora, <a href="/A254363/a254363_1.pdf">Recurrence relations for partial sums of m-th powers</a>.
%H A254363 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A254363 From _Colin Barker_, Jan 30 2015: (Start)
%F A254363 G.f.: -(342*x^3-427*x^2+165*x-20)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)).
%F A254363 a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n > 3. (End)
%F A254363 E.g.f.: exp(x)*(exp(3*x) + 3*exp(2*x) + 6*exp(x) + 10). - _Elmo R. Oliveira_, Sep 12 2024
%t A254363 Table[4^n + 6*2^n + 3^(n + 1) + 10, {n, 0, 28}] (* _Michael De Vlieger_, Jan 30 2015 *)
%o A254363 (PARI) vector(30, n, n--; 4^n + 6*2^n + 3^(n+1) + 10) \\ _Colin Barker_, Jan 30 2015
%Y A254363 Cf. A062709, A254362, A254364.
%K A254363 nonn,easy
%O A254363 0,1
%A A254363 _Luciano Ancora_, Jan 29 2015