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 A244213 #19 Jan 14 2023 16:52:38 %S A244213 -2,3,-1,0,3,-7,14,-25,43,-72,119,-195,318,-517,839,-1360,2203,-3567, %T A244213 5774,-9345,15123,-24472,39599,-64075,103678,-167757,271439,-439200, %U A244213 710643,-1149847,1860494,-3010345,4870843,-7881192 %N A244213 Inverse binomial transform of -2 followed by A000032(n+1). %C A244213 A simple transform of a(n) is a(n) with -a(0) instead of nonzero a(0) (or -a(0) followed by a(n+1)). Example: -1 followed by A198631(n+1)/A006519(n+2). Its inverse binomial transform is -1, 3/2, -2, 9/4, -2, 3/2, -2,... = -(-1)^n*A143074(n). %C A244213 Difference table of -2 followed by A000032(n+1): %C A244213 -2, 1, 3, 4, 7, 11, 18,... %C A244213 3, 2, 1, 3, 4, 7, 11,... %C A244213 -1, -1, 2, 1, 3, 4, 7,... %C A244213 0, 3, -1, 2, 1, 3, 4,... %C A244213 3, -4, 3, -1, 2, 1, 3,... %C A244213 -7, 7, -4, 3, -1, 2, 1,... %C A244213 14, -11, 7, -4, 3, -1, 2,... %C A244213 etc. %C A244213 a(n) is the first column. %H A244213 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,1). %F A244213 a(n) = -2, 3, -1, followed by -(-1)^n*A206417(n). %F A244213 a(n) = (-1)^n* (A000032(n) - 4). %F A244213 a(n+3) = -a(n) -(-1)^n*A022112(n). %F A244213 a(n) = -2*a(n-1) + a(n-3). - _Colin Barker_, Jun 23 2014 %F A244213 G.f.: -(5*x^2-x-2) / ((x+1)*(x^2-x-1)). - _Colin Barker_, Jun 23 2014 %o A244213 (PARI) Vec(-(5*x^2-x-2)/((x+1)*(x^2-x-1)) + O(x^100)) \\ _Colin Barker_, Jun 23 2014 %Y A244213 Cf. A000045, A000032, A000204. %K A244213 sign,easy %O A244213 0,1 %A A244213 _Paul Curtz_, Jun 23 2014