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A105755
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Lucas 9-step numbers.
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5
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1, 3, 7, 15, 31, 63, 127, 255, 511, 1013, 2025, 4047, 8087, 16159, 32287, 64511, 128895, 257535, 514559, 1028105, 2054185, 4104323, 8200559, 16384959, 32737631, 65410751, 130692607, 261127679, 521740799, 1042453493, 2082852801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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
| T. D. Noe, Table of n, a(n) for n=1..200
Eric Weisstein's World of Mathematics, Lucas n-Step Number
Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1)
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FORMULA
| a(n) = sum(k=1..9, a(n-k) ) for n>0, a(0)=9, a(n)=-1 for n=-8..-1
G.f. -x*(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9 ). - R. J. Mathar, Jun 20 2011
a(n)=n*sum(k=1..n, sum(i=0..(n-k)/9, (-1)^i*binomial(k,k-i)*binomial(n-9*i-1,k-1))/k). [From Vladimir Kruchinin, Aug 10 2011]
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MATHEMATICA
| a={-1, -1, -1, -1, -1, -1, -1, -1, 9}; Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 50}]
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PROG
| (Maxima)
a(n):=n*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-9*i-1, k-1), i, 0, (n-k)/9)/k, k, 1, n);
makelist(a(n), n, 1, 17); [From Vladimir Kruchinin, Aug 10 2011]
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CROSSREFS
| Cf. A000032, A001644, A073817, A074048, A074584, A104621, A105754 (Lucas n-step numbers).
Sequence in context: A105754 A116690 A043755 * A043764 A097002 A060152
Adjacent sequences: A105752 A105753 A105754 * A105756 A105757 A105758
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Apr 22 2005
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