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Padovan-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-2) + a(n-3).
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%I #23 Jul 21 2020 19:54:22

%S 2,1,1,3,2,4,5,6,9,11,15,20,26,35,46,61,81,107,142,188,249,330,437,

%T 579,767,1016,1346,1783,2362,3129,4145,5491,7274,9636,12765,16910,

%U 22401,29675,39311,52076,68986,91387,121062,160373,212449,281435,372822,493884,654257

%N Padovan-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-2) + a(n-3).

%D Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.

%H Michael De Vlieger, <a href="/A141038/b141038.txt">Table of n, a(n) for n = 0..8188</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1).

%F From _R. J. Mathar_, Oct 13 2008: (Start)

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

%F a(n)= 2*A000931(n+5) - A000931(n+4). (End)

%t Nest[Append[#, #[[-2]] + #[[-3]]] &, {2, 1, 1}, 46] (* or *)

%t CoefficientList[Series[(1 + x) (2 - x)/(1 - x^2 - x^3), {x, 0, 48}], x] (* _Michael De Vlieger_, Dec 17 2017 *)

%t LinearRecurrence[{0,1,1},{2,1,1},60] (* _Harvey P. Dale_, Jul 21 2020 *)

%o (MATLAB) function y=fib(n)

%o fz(1)=2;fz(2)=1;fz(3)=1;

%o for k=4:n

%o fz(k)=fz(k-2)+fz(k-3);

%o end

%o y=fz(n);

%o (PARI) x='x+O('x^99); Vec((1+x)*(2-x)/(1-x^2-x^3)) \\ _Altug Alkan_, Dec 17 2017

%Y Cf. A000931 (Padovan sequence).

%K nonn,easy

%O 0,1

%A Matt Wynne (mattwyn(AT)verizon.net), Jul 30 2008

%E Better name from _T. D. Noe_, Aug 06 2008

%E Offset corrected by _R. J. Mathar_, Sep 27 2009