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A097596 An A001644 Binet like function for a Bonacci 3 type sequence using two negative roots instead of all positive. 0
1, 1, 2, 4, 7, 14, 26, 48, 89, 165, 304, 559, 1029, 1893, 3482, 6404, 11779, 21666, 39850, 73296, 134813, 247961, 456072, 838847, 1542881, 2837801, 5219530, 9600212, 17657543, 32477286, 59735042, 109869872, 202082201, 371687117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..34.

FORMULA

a(n) = (r3^n-r2^n-r1^n)/(r3-r2-r1) r1=-0.419643377607080569`-0.606290729207199419` I r2=-0.419643377607080569`+0.606290729207199419` I r3=1.83928675521416113`

Empirical G.f.: x*(x^9-x^7+x^6+x^5-x+1) / ((x-1)*(x^2+1)*(x^3+x^2+x-1)*(x^4-x^2+1)). [Colin Barker, Dec 02 2012]

MATHEMATICA

NSolve[x^3-x^2-x-1==0, x] r1=-0.419643377607080569`-0.606290729207199419` I r2=-0.419643377607080569`+0.606290729207199419` I r3=1.83928675521416113` (* Binet like formula for the Bonacci 3*) f[n_]=(r3^n-r2^n-r1^n)/(r3-r2-r1) a=Table[Floor[f[n]], {n, 1, 50}]

CROSSREFS

Cf. A001644.

Sequence in context: A220842 A026010 A088813 * A054191 A257792 A079975

Adjacent sequences:  A097593 A097594 A097595 * A097597 A097598 A097599

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Sep 20 2004

STATUS

approved

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Last modified May 28 10:32 EDT 2020. Contains 334681 sequences. (Running on oeis4.)