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 A106392 #50 Mar 19 2020 13:41:13
%S A106392 1,6,26,96,316,936,2456,5376,7696,-7584,-122464,-658944,-2729024,
%T A106392 -9784704,-31417984,-90660864,-229785344,-472103424,-534767104,
%U A106392 1512431616,14422260736,71409248256,284232882176,991304810496,3105500041216,8719952142336,21264712441856,40388753227776
%N A106392 Expansion of 1/(1 - 6*x + 10*x^2).
%C A106392 In general, the sequence with g.f. 1/(1 - 2r*x + (r^2 + 1)*x^2) = 1/((1 - r*x)^2 + x^2) has a(n) = Sum_{k = 0..floor(n/2)} binomial(n - k, k)(r^2 - 1)^k*(2r)^(n - 2k); a(n) = Sum_{k = 0..floor((n + 1)/2)} binomial(n + 1, 2k + 1)(-1)^k*r^(n-2k).
%H A106392 Robert Israel, <a href="/A106392/b106392.txt">Table of n, a(n) for n = 0..1997</a>
%H A106392 Beata Bajorska-Harapińska, Barbara Smoleń, Roman Wituła, <a href="https://doi.org/10.1007/s00006-019-0969-9">On Quaternion Equivalents for Quasi-Fibonacci Numbers, Shortly Quaternaccis</a>, Advances in Applied Clifford Algebras (2019) Vol. 29, 54.
%H A106392 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-10).
%F A106392 G.f.: 1/((1 - 3*x)^2 + x^2).
%F A106392 a(n) = Sum_{k = 0..floor(n/2)} binomial(n - k, k)(-10)^k*6^(n - 2k).
%F A106392 a(n) = Sum_{k = 0..floor((n + 1)/2)} binomial(n + 1, 2k + 1)(-1)^k*3^(n - 2k).
%F A106392 a(n) = 6*a(n - 1) - 10*a(n - 2), n >= 2. - _Vincenzo Librandi_, Mar 22 2011
%F A106392 a(n) = Im((3 + i)^(n + 1)), where i = sqrt(-1). - _César Eliud Lozada_, Sep 19 2012
%F A106392 E.g.f.: (3*sin(x) + cos(x))*exp(3*x). - _Ilya Gutkovskiy_, Nov 25 2016
%p A106392 f:= gfun:- rectoproc({a(n+2)=6*a(n+1)-10*a(n),a(0)=1,a(1)=6},a(n),remember):
%p A106392 map(f, [$0..50]); # _Robert Israel_, Nov 25 2016
%t A106392 CoefficientList[Series[1/(1 - 6x + 10x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -10}, {1, 6}, 30] (* _Harvey P. Dale_, Feb 05 2015 *)
%o A106392 (Sage) [lucas_number1(n,6,10) for n in range(1, 29)] # _Zerinvary Lajos_, Apr 22 2009
%o A106392 (PARI) imag((3+I)^(n+1)); /* _Joerg Arndt_, Sep 20 2012 */
%o A106392 (PARI) x='x+O('x^100); Vec(1/((1-3*x)^2+x^2)) \\ _Altug Alkan_, Dec 24 2015
%K A106392 easy,sign
%O A106392 0,2
%A A106392 _Paul Barry_, May 01 2005