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 A157517 #11 Sep 08 2022 08:45:42 %S A157517 7,13,7,-11,-41,-83,-137,-203,-281,-371,-473,-587,-713,-851,-1001, %T A157517 -1163,-1337,-1523,-1721,-1931,-2153,-2387,-2633,-2891,-3161,-3443, %U A157517 -3737,-4043,-4361,-4691,-5033,-5387,-5753,-6131,-6521,-6923,-7337,-7763,-8201,-8651 %N A157517 a(n) = 7 + 12*n - 6*n^2. %C A157517 From John Couch Adams multisteps integration of differential equations, 1855. %D A157517 P. Curtz Integration numerique des systemes differentiels, C.C.S.A., Arcueil, 1969, p. 36. %H A157517 Vincenzo Librandi, <a href="/A157517/b157517.txt">Table of n, a(n) for n = 0..10000</a> %H A157517 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A157517 a(n) = 12*n + 6 - A140811(n) = A017593(n) - A140811(n). %F A157517 Recurrences: a(n) = 2*a(n-1) - a(n-2) - 12 = 3*a(n-1) - 3*a(n-2) + a(n-3). %F A157517 First differences: a(n+1) - a(n) = -A017593(n-1), n > 0. Second differences are all -12. %F A157517 a(n+2) - a(n) = -A008606(n). %F A157517 G.f.: (-7 + 8*x + 11*x^2)/(x-1)^3. - _R. J. Mathar_, Mar 15 2009 %o A157517 (Magma) [7+12*n-6*n^2: n in [0..50]]; // _Vincenzo Librandi_, Aug 07 2011 %o A157517 (PARI) a(n)=7+12*n-6*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017 %K A157517 sign,easy %O A157517 0,1 %A A157517 _Paul Curtz_, Mar 02 2009 %E A157517 Edited and extended by _R. J. Mathar_, Mar 15 2009