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