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 A135247 #45 May 20 2024 02:13:37
%S A135247 1,3,11,33,103,309,935,2805,8431,25293,75911,227733,683263,2049789,
%T A135247 6149495,18448485,55345711,166037133,498111911,1494335733,4483008223,
%U A135247 13449024669,40347076055,121041228165,363123688591,1089371065773,3268113205511,9804339616533
%N A135247 a(n) = 3*a(n-1) + 2*a(n-2) - 6*a(n-3).
%C A135247 This sequence interleaves A016133 and 3*A016133, see formulas. - _Mathew Englander_, Jan 08 2024
%C A135247 a(n) is the number of partitions of n into parts 1 (in three colors) and 2 (in two colors) where the order of colors matters. For example, the a(2)=11 such partitions (using parts 1, 1', 1'', 2, and 2') are 2, 2', 1+1, 1+1', 1+1'', 1'+1, 1'+1', 1'+1'', 1''+1, 1''+1', 1''+1''. For such partitions where the order of colors does not matter see A002624. - _Joerg Arndt_, Jan 18 2024
%H A135247 Sean A. Irvine, <a href="/A135247/b135247.txt">Table of n, a(n) for n = 0..1000</a>
%H A135247 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-6).
%F A135247 G.f.: 1/((1-3*x)*(1-2*x^2)). - _G. C. Greubel_, Oct 04 2016
%F A135247 From _Mathew Englander_, Jan 08 2024: (Start)
%F A135247 a(n) = A010684(n) * A016133(floor(n/2)).
%F A135247 a(n) = 3*a(n-1) + A077957(n) for n >= 1.
%F A135247 a(n) = (A000244(n+2) - A164073(n+3))/7.
%F A135247 (End)
%p A135247 seq(coeff(series(1/(1-3*x-2*x^2+6*x^3), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Nov 20 2019
%t A135247 LinearRecurrence[{3,2,-6},{1,3,11},30] (* _Harvey P. Dale_, Jun 27 2015 *)
%o A135247 (PARI) my(x='x+O('x^30)); Vec(1/(1-3*x-2*x^2+6*x^3)) \\ _G. C. Greubel_, Nov 20 2019
%o A135247 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-3*x-2*x^2+6*x^3) )); // _G. C. Greubel_, Nov 20 2019
%o A135247 (Sage)
%o A135247 def A135247_list(prec):
%o A135247 P.<x> = PowerSeriesRing(ZZ, prec)
%o A135247 return P( 1/(1-3*x-2*x^2+6*x^3) ).list()
%o A135247 A135247_list(30) # _G. C. Greubel_, Nov 20 2019
%o A135247 (GAP) a:=[1,3,11];; for n in [4..30] do a[n]:=3*a[n-1]+2*a[n-2]-6*a[n-3]; od; a; # _G. C. Greubel_, Nov 20 2019
%Y A135247 Cf. A016133.
%K A135247 nonn,easy
%O A135247 0,2
%A A135247 _Paul Curtz_, Feb 15 2008
%E A135247 More terms from _Harvey P. Dale_, Jun 27 2015
%E A135247 Dropped two leading terms = 0. - _Joerg Arndt_, Jan 18 2024