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%I #20 Sep 08 2022 08:45:10
%S 1,1,17,-47,545,-3167,24113,-162959,1158209,-8054975,56542289,
%T -395323631,2768682593,-19376526623,135648440945,-949500822863,
%U 6646620551297,-46525999485311,325683029518481,-2279778107265455,15958456048949921,-111709164448374239
%N a(n) = (4*3^n + (-7)^n)/5.
%C Binomial transform of A083295.
%D K. H. Rosen, Handbook of Discrete and Combinatorial Mathematics, CRC Press LLC, 2000, p. 182 (example 9).
%H Vincenzo Librandi, <a href="/A083296/b083296.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-4,21).
%F G.f.: (1+5*x)/((1-3*x)*(1+7*x)).
%F E.g.f.: (4*exp(3*x) + exp(-7*x))/5.
%t Table[[(4*3^n+(-7)^n)/5], {n,0,21}] (* _Bruno Berselli_, Dec 06 2011 *)
%t LinearRecurrence[{-4,21},{1,1},30] (* _Harvey P. Dale_, Dec 13 2015 *)
%o (Magma) [(4*3^n+(-7)^n)/5: n in [0..30]]; // _Vincenzo Librandi_, Jun 08 2011
%o (Maxima) a[0]:1$ a[1]:1$ a[n]:=-4*a[n-1]+21*a[n-2]$ makelist(a[n], n, 0, 21); /* _Bruno Berselli, Dec 06 2011 */
%o (PARI) a(n)=(4*3^n+(-7)^n)/5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A083297.
%K sign,easy
%O 0,3
%A _Paul Barry_, Apr 24 2003
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