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 A111642 #10 Mar 11 2024 03:48:12 %S A111642 2,-12,54,-224,890,-3452,13198,-50016,188498,-707916,2652678,-9925760, %T A111642 37105802,-138631292,517742494,-1933118784,7216615970,-26937891852, %U A111642 100545928278,-375272321696,1400607336218,-5227311479036,19509011469358,-72809634633120,271731700422002 %N A111642 Expansion of 2*(x-1)*(x+1)/((x^2+4*x+1)*(x^2-2*x-1)). %C A111642 In reference to the program code, the sequence of Pell numbers A000126 is given by 1kbaseseq[C*J]. A001353 is 1ibaseiseq[C*J]. %C A111642 Floretion Algebra Multiplication Program, FAMP Code: 1ibaseseq[C*J] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and J = + j' + k' + 1.5'ii' + .5'jj' + .5'kk' + .5e %H A111642 Colin Barker, <a href="/A111642/b111642.txt">Table of n, a(n) for n = 0..1000</a> %H A111642 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-8,2,1). %F A111642 a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3. - _Colin Barker_, Apr 29 2019 %o A111642 (PARI) Vec(2*(1 - x)*(1 + x) / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^25)) \\ _Colin Barker_, Apr 29 2019 %Y A111642 Cf. A111639, A111640, A111641, A111643, A111644, A000126. %K A111642 easy,sign %O A111642 0,1 %A A111642 _Creighton Dement_, Aug 10 2005