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 A162557 #30 Sep 08 2022 08:45:46
%S A162557 1,5,27,151,857,4893,28003,160415,919281,5268853,30200171,173106279,
%T A162557 992248009,5687602445,32601595443,186873931759,1071170713313,
%U A162557 6140004593637,35194817476027,201738480090935,1156375213539129,6628401467130877,37994333961038339,217785452615605311
%N A162557 a(n) = ((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)/6.
%C A162557 Binomial transform of A086405.
%C A162557 Inverse binomial transform of A162558.
%C A162557 4th binomial transform of A108411.
%C A162557 2nd binomial transform of A079935. [_R. J. Mathar_, Jul 17 2009]
%C A162557 From _J. Conrad_, Aug 29 2016: (Start)
%C A162557 Partial sum of A136777.
%C A162557 Backward difference of Sum_{k=0..n} A027907(n+1,2k+2)*3^k.
%C A162557 (End)
%C A162557 String length in substitution system {0 -> 1001001, 1 -> 11011} at step n from initial string "1" (1 -> 11011 -> 110111101110010011101111011 -> ...). - _Ilya Gutkovskiy_, Aug 30 2016
%H A162557 Harvey P. Dale, <a href="/A162557/b162557.txt">Table of n, a(n) for n = 0..1000</a>
%H A162557 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).
%F A162557 a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
%F A162557 G.f.: (1-3*x)/(1-8*x+13*x^2).
%p A162557 seq(simplify(((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)*1/6), n = 0..20); # _Emeric Deutsch_, Jul 14 2009
%t A162557 Table[FullSimplify[((3 + #) (4 + #)^n + (3 - #) (4 - #)^n)/6 &@ Sqrt@ 3], {n, 0, 23}] (* _Michael De Vlieger_, Aug 30 2016 *)
%t A162557 LinearRecurrence[{8,-13},{1,5},30] (* _Harvey P. Dale_, Oct 23 2020 *)
%o A162557 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/6: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 13 2009
%o A162557 (Magma) I:=[1,5]; [n le 2 select I[n] else 8*Self(n-1)-13*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Aug 30 2016
%Y A162557 Cf. A108411 (powers of 3 repeated), A086405, A162558.
%Y A162557 Cf. A162558. [_R. J. Mathar_, Jul 17 2009]
%K A162557 nonn
%O A162557 0,2
%A A162557 Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
%E A162557 Edited, corrected and extended beyond a(5) by _Klaus Brockhaus_, _Emeric Deutsch_ and _R. J. Mathar_, Jul 07 2009
%E A162557 More terms from _Vincenzo Librandi_, Aug 30 2016