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a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.
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%I #13 Apr 10 2024 04:41:28

%S 1,2,5,14,39,108,299,828,2293,6350,17585,48698,134859,373464,1034231,

%T 2864088,7931497,21964634,60826493,168446342,466477167,1291811652,

%U 3577404131,9906877908,27435041245,75975649958,210398786537

%N a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,1).

%F G.f.: (1-x)/(1-3*x+x^2-x^3).

%F a(n) = A200752(n+3) - A200752(n+2). - _R. J. Mathar_, Dec 15 2011

%o (PARI) my(x='x+O('x^40)); Vec((1-x)/(1-3*x+x^2-x^3)) \\ _Michel Marcus_, Apr 10 2024

%Y Cf. A200752.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Dec 14 2011