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 A120743 #41 Mar 11 2024 20:53:31
%S A120743 1,-8,-26,28,316,352,-2456,-8432,7696,99712,122464,-752192,-2729024,
%T A120743 2063872,31417984,42197248,-229785344,-881543168,534767104,9884965888,
%U A120743 14422260736,-70005137408,-284232882176,131585609728,3105500041216
%N A120743 a(n) = (1/2)*(1 + 3*i)^n + (1/2)*(1 - 3*i)^n where i = sqrt(-1).
%C A120743 From _R. J. Mathar_, Jun 15 2007: (Start)
%C A120743 These are the row sums of the triangle A013610 after every 2nd column is deleted, then every 2nd column reversed in sign, creating an intermediate irregular triangle with entries C(n,2*k)*(-9)^k, k = 0..floor(n/2):
%C A120743 1;
%C A120743 1, -9;
%C A120743 1, -27;
%C A120743 1, -54, 81;
%C A120743 1, -90, 405;
%C A120743 1, -135, 1215, -729;
%C A120743 1, -189, 2835, -5103;
%C A120743 1, -252, 5670, -20412, 6561;
%C A120743 1, -324, 10206, -61236, 59049;
%C A120743 1, -405, 17010, -153090, 295245, -59049; (End)
%C A120743 Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[A*B] with A = + 1.5i' + .5j' + .5k' + .5e and B = 'ji' + e
%H A120743 Vincenzo Librandi, <a href="/A120743/b120743.txt">Table of n, a(n) for n = 1..100</a>
%H A120743 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -10).
%F A120743 a(n) = 2*a(n-1) - 10*a(n-2).
%F A120743 G.f.: x*(1-10*x)/(10*x^2 - 2*x + 1).
%F A120743 a(n) mod 9 = 1. - _Paul Curtz_, Apr 20 2011
%F A120743 G.f.: G(0)/(2*x) - 1/x, where G(k) = 1 + 1/(1 - x*(9*k+1)/(x*(9*k+10) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, May 29 2013
%F A120743 E.g.f.: exp(x)*cos(3*x). - _Sergei N. Gladkovskii_, May 29 2013
%F A120743 a(n) = A190958(n)-10*A190958(n-1). - _R. J. Mathar_, Dec 13 2022
%t A120743 LinearRecurrence[{2,-10}, {1,-8}, 30] (* _G. C. Greubel_, Nov 09 2018 *)
%o A120743 (Magma) [ n eq 1 select 1 else n eq 2 select -8 else 2*Self(n-1) -10*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Aug 24 2011
%o A120743 (PARI) x='x+O('x^30); Vec((1-10*x)/(1-2*x+10*x^2)) \\ _G. C. Greubel_, Nov 09 2018
%Y A120743 Cf. A006495
%K A120743 easy,sign
%O A120743 1,2
%A A120743 _Creighton Dement_, Jun 11 2007
%E A120743 a(0)=1: a(n) is main diagonal of A009116(n). - _Paul Curtz_, Jul 22 2011
%E A120743 Edited by _Jon E. Schoenfield_, Nov 09 2018