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A168637 a(n) = a(n-1) + a(n-2) - a(n-4) starting a(0)=0, a(1)=1, a(2)=a(3)=3. 1
0, 1, 3, 3, 6, 8, 11, 16, 21, 29, 39, 52, 70, 93, 124, 165, 219, 291, 386, 512, 679, 900, 1193, 1581, 2095, 2776, 3678, 4873, 6456, 8553, 11331, 15011, 19886, 26344, 34899, 46232, 61245, 81133, 107479, 142380, 188614, 249861, 330996, 438477, 580859, 769475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The limiting ratio a(n+1)/a(n) is the same as with A000931, which is A060006.

REFERENCES

R. Pallu de la Barriere, Optimal Control Theory, Dover Publications, New York, 1967, pages 339-344

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: x*(1 + 2*x - x^2)/((1-x)*(1 - x^2 - x^3)). [Dec 03 2009]

a(n) = 3*A000931(n+4) + 2*A000931(n+3) - 2. [Dec 03 2009]

a(n) = a(n-2) + a(n-3) + 2. - Greg Dresden, May 18 2020

MATHEMATICA

LinearRecurrence[{1, 1, 0, -1}, {0, 1, 3, 3}, 50] (* or *) CoefficientList[ Series[ x*(-1-2x+x^2)/((1-x)(x^3+x^2-1)), {x, 0, 50}], x] (* Harvey P. Dale, Jun 22 2011 *)

PROG

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 1, 1]^n*[0; 1; 3; 3])[1, 1] \\ Charles R Greathouse IV, Jul 29 2016

CROSSREFS

Cf. A007307 (for a different starting vector of the Mma program).

Sequence in context: A049626 A241343 A309455 * A241390 A241831 A239946

Adjacent sequences:  A168634 A168635 A168636 * A168638 A168639 A168640

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Dec 01 2009

EXTENSIONS

Precise definition and more formulas supplied by the Assoc. Editors of the OEIS, Dec 03 2009

STATUS

approved

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Last modified July 12 00:27 EDT 2020. Contains 335658 sequences. (Running on oeis4.)