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Search: id:A073817
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| A073817 |
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Tetranacci numbers with different initial conditions a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4), a(0)=4, a(1)=1, a(2)=3, a(4)=7. |
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31
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| 4, 1, 3, 7, 15, 26, 51, 99, 191, 367, 708, 1365, 2631, 5071, 9775, 18842, 36319, 70007, 134943, 260111, 501380, 966441, 1862875, 3590807, 6921503, 13341626, 25716811, 49570747, 95550687, 184179871, 355018116, 684319421, 1319068095, 2542585503
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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These tetranacci numbers follow the same pattern as Lucas and generalized tribonacci(A001644) numbers: Binet's formula is a(n)=r1^n+r^2^n+r3^n+r4^n, with r1, r2, r3, r4 roots of the characteristic polynomial.
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REFERENCES
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Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
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LINKS
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E. Weisstein, Fibonacci n-Step
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FORMULA
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G.f.: (4-3x-2x^2-x^3)/(1-x-x^2-x^3-x^4)
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MATHEMATICA
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CoefficientList[Series[(4-3x-2x^2-x^3)/(1-x-x^2-x^3-x^4), {x, 0, 40}], x]
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CROSSREFS
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Cf. A000078, A001630, A001644, A000032. Two other versions: A001648, A074081.
Sequence in context: A121441 A074813 A109531 this_sequence A074081 A132703 A093735
Adjacent sequences: A073814 A073815 A073816 this_sequence A073818 A073819 A073820
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Aug 12 2002
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