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 A138635 #17 Sep 27 2024 02:51:35 %S A138635 0,0,1,0,1,1,1,2,1,3,3,2,6,5,5,11,10,11,21,21,22,42,43,43,85,86,85, %T A138635 171,171,170,342,341,341,683,682,683,1365,1365,1366,2730,2731,2731, %U A138635 5461,5462,5461,10923,10923,10922,21846,21845,21845,43691,43690,43691,87381 %N A138635 a(n) =3*a(n-3)-3*a(n-6)+2*a(n-9). %C A138635 As the recurrence shows, these are three interleaved sequences which obey recurrences b(n)=3*b(n-1)-3*b(n-2)+2*b(n-3), indicating that the b(n) equal their third differences. %C A138635 These three sequences are A024495, A024494 (or A131708) and A024493 (or A130781). %C A138635 Their starting "vectors" b(0,1,2) are 0,0,1 and 0,1,2 and 1,1,1, respectively, therefore linearly independent, such that other sequences with the same recursion as b(n) can be written as linear combinations of these. %H A138635 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,2). %F A138635 a(18*n) = 21*A133853(n). %F A138635 G.f.: -x^2*(1+x^2-2*x^3+x^4-x^5+x^6)/((2*x^3-1)*(x^6-x^3+1)). - _R. J. Mathar_, May 17 2009 %Y A138635 Cf. A024493, A024494, A024495, A131708, A130781. %K A138635 nonn,easy %O A138635 0,8 %A A138635 _Paul Curtz_, May 14 2008 %E A138635 Edited by _R. J. Mathar_, May 17 2009