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Search: id:A074048
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| A074048 |
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Pentanacci numbers with initial conditions a(0)=5, a(1)=1, a(2)=3, a(3)=7, a(4)=15. |
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+0
28
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| 5, 1, 3, 7, 15, 31, 57, 113, 223, 439, 863, 1695, 3333, 6553, 12883, 25327, 49791, 97887, 192441, 378329, 743775, 1462223, 2874655, 5651423, 11110405, 21842481, 42941187, 84420151, 165965647, 326279871, 641449337
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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These pentanacci numbers follow the same pattern as Lucas, generalized tribonacci(A001644) and generalized tetranacci (A73817) numbers: Binet's formula is a(n)=r1^n+r^2^n+r3^n+r4^n+r5^n, with r1, r2, r3, r4, r5 roots of the characteristic polynomial. a(n) is also the trace of A^n, where A is the pentamatrix ((1,1,0,0,0),(1,0,1,0,0),(1,0,0,1,0),(1,0,0,0,1),(1,0,0,0,0)).
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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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Index entries for sequences related to linear recurrences with constant coefficients
E. Weisstein, Fibonacci n-Step
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FORMULA
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a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5). G.f.: (5-4x-3x^2-2x^3-x^4)/(1-x-x^2-x^3-x^4-x^5)
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MATHEMATICA
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CoefficientList[Series[(5-4*x-3*x^2-2*x^3-x^4)/(1-x-x^2-x^3-x^4-x^5), {x, 0, 30}], x]
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CROSSREFS
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Cf. A000078, A001630, A001644, A000032, A073817.
Essentially the same as A023424.
Sequence in context: A053544 A094136 A051996 this_sequence A134894 A143700 A036790
Adjacent sequences: A074045 A074046 A074047 this_sequence A074049 A074050 A074051
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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 14 2002
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