OFFSET
0,2
COMMENTS
Companion sequence A121621 is real((2 + 3i)^n).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..500
Beata Bajorska-Harapińska, Barbara Smoleń, and Roman Wituła, On Quaternion Equivalents for Quasi-Fibonacci Numbers, Shortly Quaternaccis, Advances in Applied Clifford Algebras (2019) Vol. 29, 54.
Index entries for linear recurrences with constant coefficients, signature (6,-13).
FORMULA
a(n) = real((3 + 2i)^n).
a(n) = 6*a(n-1) - 13*a(n-2).
G.f.: ( 1-3*x ) / ( 1-6*x+13*x^2 ). - R. J. Mathar, Aug 12 2012
E.g.f.: exp(3*x)*cos(2*x). - Sergei N. Gladkovskii, Jan 20 2014
EXAMPLE
a(5) = -597 since (3 + 2i)^5 = (-597 + 122i).
a(5) = -597 = 6*(-119) - 13*(-9) = 6*a(5) -13*a(4).
MATHEMATICA
f[n_] := Re[(3 + 2I)^n]; Table[f[n], {n, 0, 24}] (* Robert G. Wilson v, Aug 17 2006 *)
LinearRecurrence[{6, -13}, {1, 3}, 30] (* Harvey P. Dale, Apr 24 2017 *)
PROG
(PARI) a(n) = real((3 + 2*I)^n); \\ Michel Marcus, Jun 12 2021
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Gary W. Adamson and Nick Williams, Aug 10 2006
EXTENSIONS
More terms from Robert G. Wilson v, Aug 17 2006
STATUS
approved