A141038 Padovan-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-2) + a(n-3).

2, 1, 1, 3, 2, 4, 5, 6, 9, 11, 15, 20, 26, 35, 46, 61, 81, 107, 142, 188, 249, 330, 437, 579, 767, 1016, 1346, 1783, 2362, 3129, 4145, 5491, 7274, 9636, 12765, 16910, 22401, 29675, 39311, 52076, 68986, 91387, 121062, 160373, 212449, 281435, 372822, 493884, 654257

Offset

0,1

References

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

Links

Michael De Vlieger, Table of n, a(n) for n = 0..8188

Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Formula

From R. J. Mathar, Oct 13 2008: (Start)

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

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

Mathematica

Nest[Append[#, #[[-2]] + #[[-3]]] &, {2, 1, 1}, 46] (* or *)
CoefficientList[Series[(1 + x) (2 - x)/(1 - x^2 - x^3), {x, 0, 48}], x] (* Michael De Vlieger, Dec 17 2017 *)
LinearRecurrence[{0, 1, 1}, {2, 1, 1}, 60] (* Harvey P. Dale, Jul 21 2020 *)

Prog

(MATLAB) function y=fib(n)
fz(1)=2; fz(2)=1; fz(3)=1;
for k=4:n
fz(k)=fz(k-2)+fz(k-3);
end
y=fz(n);
(PARI) x='x+O('x^99); Vec((1+x)*(2-x)/(1-x^2-x^3)) \\ Altug Alkan, Dec 17 2017

Crossrefs

Cf. A000931 (Padovan sequence).

Sequence in context: A117334 A241472 A071872 * A240055 A156309 A205115

Adjacent sequences: A141035 A141036 A141037 * A141039 A141040 A141041

Keyword

nonn,easy

Author

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

Extensions

Better name from T. D. Noe, Aug 06 2008

Offset corrected by R. J. Mathar, Sep 27 2009

Status

approved