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 A179608 #15 Jul 03 2023 11:37:26 %S A179608 1,3,10,24,64,144,352,768,1792,3840,8704,18432,40960,86016,188416, %T A179608 393216,851968,1769472,3801088,7864320,16777216,34603008,73400320, %U A179608 150994944,318767104,654311424,1375731712,2818572288,5905580032 %N A179608 a(n) = (7 + (-1)^n + 6*n)*2^(n-3). %C A179608 This sequence belongs to a family of sequences with g.f. (1+x)/(1 - 2*x - (k+8)*x^2 - 2*k*x^3). Among the members of this family are several red king sequences, see A179596. For the sequence given above, which is not a red king sequence, k = -4. %C A179608 Inverse binomial transform of A119916 (without the leading 0). %H A179608 Vincenzo Librandi, <a href="/A179608/b179608.txt">Table of n, a(n) for n = 0..1000</a> %H A179608 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 4, -8). %F A179608 G.f.: (1+x)/(1 - 4*x^2 - 2*x + 8*x^3). %F A179608 a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) with a(1)=1, a(2)=3 and a(3)=10. %F A179608 a(n) = (7 + (-1)^n + 6*n)*2^(n-3). %o A179608 (Magma) [(7+(-1)^n+6*n)*2^(n-3): n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011 %K A179608 easy,nonn %O A179608 0,2 %A A179608 _Johannes W. Meijer_, Jul 28 2010