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%I #36 Dec 31 2023 11:29:36
%S 1,3,5,-9,-119,-597,-2035,-4449,-239,56403,341525,1315911,3455641,
%T 3627003,-23161315,-186118929,-815616479,-2474152797,-4241902555,
%U 6712571031,95420159401,485257533003,1671083125805,3718150825791,584824319281
%N Real part of (3 + 2i)^n.
%C Companion sequence A121621 is real((2 + 3i)^n).
%H Michael De Vlieger, <a href="/A121622/b121622.txt">Table of n, a(n) for n = 0..500</a>
%H Beata Bajorska-Harapińska, Barbara Smoleń, and 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13).
%F a(n) = real((3 + 2i)^n).
%F a(n) = 6*a(n-1) - 13*a(n-2).
%F G.f.: ( 1-3*x ) / ( 1-6*x+13*x^2 ). - _R. J. Mathar_, Aug 12 2012
%F E.g.f.: exp(3*x)*cos(2*x). - _Sergei N. Gladkovskii_, Jan 20 2014
%e a(5) = -597 since (3 + 2i)^5 = (-597 + 122i).
%e a(5) = -597 = 6*(-119) - 13*(-9) = 6*a(5) -13*a(4).
%t f[n_] := Re[(3 + 2I)^n]; Table[f[n], {n, 0, 24}] (* _Robert G. Wilson v_, Aug 17 2006 *)
%t LinearRecurrence[{6,-13},{1,3},30] (* _Harvey P. Dale_, Apr 24 2017 *)
%o (PARI) a(n) = real((3 + 2*I)^n); \\ _Michel Marcus_, Jun 12 2021
%Y Cf. A121621.
%Y Cf. A193410, A066771.
%K sign,easy
%O 0,2
%A _Gary W. Adamson_ and Nick Williams, Aug 10 2006
%E More terms from _Robert G. Wilson v_, Aug 17 2006
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