|
%I #20 Sep 08 2022 08:45:11
%S 1,2,5,13,35,97,275,793,2315,6817,20195,60073,179195,535537,1602515,
%T 4799353,14381675,43112257,129271235,387682633,1162785755,3487832977,
%U 10462450355,31385253913,94151567435,282446313697,847322163875
%N Expansion of (1 - 3*x + x^2)/((1-2*x)*(1-3*x)).
%C Binomial transform of A005578. Binomial transform is A085282.
%H Vincenzo Librandi, <a href="/A085281/b085281.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6).
%F a(n) = 3^n/3 + 2^n/2 + 0^n/6.
%F a(n) = A007689(n-1), n > 0. - _R. J. Mathar_, Sep 12 2008
%t a[n_]:=3^n/3 + 2^n/2; Flatten[Join[{1, Array[a, 50]}]] (* or *)
%t CoefficientList[Series[(1 - 3*x + x^2)/((1-2*x)*(1-3*x)), {x, 0, 50}], x] (* _Stefano Spezia_, Sep 09 2018 *)
%t LinearRecurrence[{5,-6},{1,2,5},30] (* _Harvey P. Dale_, Jun 14 2022 *)
%o (Magma) [3^n/3+2^n/2+0^n/6: n in [0..35]]; // _Vincenzo Librandi_, May 29 2011
%Y Cf. A005578, A007689, A085282.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 25 2003
|
