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 A164037 #20 Mar 17 2024 02:12:06
%S A164037 5,21,91,399,1757,7749,34195,150927,666197,2940693,12980779,57299823,
%T A164037 252933485,1116502149,4928478499,21755355951,96032786213,423909225621,
%U A164037 1871225850235,8259990522063,36461362180733,160948239429957
%N A164037 Expansion of (5-9*x)/(1-6*x+7*x^2).
%C A164037 Binomial transform of A161941 without initial 2. Third binomial transform of A164095. Inverse binomial transform of A161731 without initial 1.
%H A164037 G. C. Greubel, <a href="/A164037/b164037.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%H A164037 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-7).
%F A164037 a(n) = 6*a(n-1)-7*a(n-2) for n > 1; a(0) = 5, a(1) = 21.
%F A164037 G.f.: (5-9*x)/(1-6*x+7*x^2).
%F A164037 a(n) = ((5+3*sqrt(2))*(3+sqrt(2))^n+(5-3*sqrt(2))*(3-sqrt(2))^n)/2.
%F A164037 E.g.f.: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - _G. C. Greubel_, Sep 08 2017
%t A164037 CoefficientList[Series[(5-9x)/(1-6x+7x^2),{x,0,30}],x] (* or *) LinearRecurrence[{6,-7},{5,21},30] (* _Harvey P. Dale_, Apr 27 2017 *)
%o A164037 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(3+r)^n+(5-3*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 10 2009
%o A164037 (PARI) Vec((5-9*x)/(1-6*x+7*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A164037 Cf. A161941, A164095 (5, 6, 10, 12, 20, 24, ...), A161731.
%K A164037 nonn,easy
%O A164037 0,1
%A A164037 Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
%E A164037 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 10 2009