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 A135264 #20 Sep 08 2022 08:45:32 %S A135264 3,12,42,123,366,1092,3279,9840,29526,88575,265722,797160,2391483, %T A135264 7174452,21523362,64570083,193710246,581130732,1743392199,5230176600, %U A135264 15690529806,47071589415,141214768242,423644304720,1270932914163 %N A135264 a(n) = 3*A132357(n). %C A135264 Digital roots yield a hexaperiodic sequence A010888(a(n))= 3*A135265(n+1). %H A135264 G. C. Greubel, <a href="/A135264/b135264.txt">Table of n, a(n) for n = 0..1000</a> %H A135264 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-1,3). %F A135264 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4). %F A135264 G.f.: 3*(1 + x + 2*x^2)/(1 - 3*x + x^3 - 3*x^4). - _G. C. Greubel_, Oct 07 2016 [corrected by _Georg Fischer_, May 10 2019] %p A135264 seq(coeff(series(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 21 2019 %t A135264 LinearRecurrence[{3,0,-1,3}, {3,12,42,123}, 25] (* _G. C. Greubel_, Oct 07 2016 *) %o A135264 (PARI) my(x='x+O('x^30)); Vec(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)) \\ _G. C. Greubel_, Nov 21 2019 %o A135264 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4) )); // _G. C. Greubel_, Nov 21 2019 %o A135264 (Sage) %o A135264 def A135264_list(prec): %o A135264 P.<x> = PowerSeriesRing(ZZ, prec) %o A135264 return P(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)).list() %o A135264 A135264_list(30) # _G. C. Greubel_, Nov 21 2019 %o A135264 (GAP) a:=[3,12,42,123];; for n in [5..30] do a[n]:=3*a[n-1]-a[n-3]+ 3*a[n-4]; od; a; # _G. C. Greubel_, Nov 21 2019 %K A135264 nonn,less,easy %O A135264 0,1 %A A135264 _Paul Curtz_, Dec 02 2007 %E A135264 Edited, corrected and extended by _R. J. Mathar_, Jul 28 2008