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 A363299 #37 Jun 02 2025 16:49:53
%S A363299 5,16,70,346,1810,9826,54850,312706,1810690,10601986,62563330,
%T A363299 371185666,2210336770,13194911746,78901035010,472332468226,
%U A363299 2829699842050,16961019183106,101697395621890,609909495824386,3658357463318530,21945746733400066,131656888214355970,789870960541958146
%N A363299 a(n) is the sum of the n-th powers of the terms of row 4 of Pascal's triangle.
%H A363299 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-34,24).
%F A363299 a(n) = 2 + 2*4^n + 6^n.
%F A363299 From _Natalia L. Skirrow_, Jun 25 2023: (Start)
%F A363299 G.f.: (5-39*x+64*x^2)/((1-x)*(1-4*x)*(1-6*x)).
%F A363299 E.g.f.: 2*e^x + 2*e^(4*x) + e^(6*x).
%F A363299 (End)
%e A363299 a(2) = 1^2 + 4^2 + 6^2 + 4^2 + 1^2 = 1 + 16 + 36 + 16 + 1 = 70.
%t A363299 Table[6^n + 2*(4^n + 1), {n, 0, 24}] (* _Amiram Eldar_, May 27 2023 *)
%o A363299 (Python)
%o A363299 def A363299(n): return 2+(((1<<n+1)+3**n)<<n) # _Chai Wah Wu_, Jun 27 2023
%Y A363299 Cf. A007318.
%Y A363299 Cf. A000012 (row 0), A007395 (row 1), A052548 (row 2), A115099 (row 3).
%K A363299 nonn,easy
%O A363299 0,1
%A A363299 _J. Lowell_, May 26 2023