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A127624
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An 11th order Fibonacci sequence. a(n) = a(n-1) + ... + a(n-11).
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8
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 21, 41, 81, 161, 321, 641, 1281, 2561, 5121, 10241, 20481, 40951, 81881, 163721, 327361, 654561, 1308801, 2616961, 5232641, 10462721, 20920321, 41830401, 83640321, 167239691, 334397501, 668631281
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OFFSET
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1,12
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COMMENTS
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The ratio a(n+1)/a(n) approaches the unique real root of r^11 = r^10 + ... + r + 1; r is about 1.99951040197828549144.
All terms have last digit 1.
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LINKS
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Robert Price, Table of n, a(n) for n = 1..1000
E. S. Croot, Notes on Linear Recurrence Sequences
M. A. Lerma, Recurrence Relations
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1,1,1).
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FORMULA
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O.g.f: x*(-1+x^2+2*x^3+3*x^4+4*x^5+5*x^6+6*x^7+7*x^8+8*x^9+9*x^10) / (-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11). - R. J. Mathar, Dec 02 2007
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MATHEMATICA
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Module[{nn=11, lr}, lr=PadRight[{}, nn, 1]; LinearRecurrence[lr, lr, 20]] (* Harvey P. Dale, Feb 04 2015 *)
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PROG
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(PARI) x='x+O('x^50); Vec(x*(-1+x^2+2*x^3+3*x^4+4*x^5+5*x^6+6*x^7+7*x^8 +8*x^9+9*x^10)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11)) \\ G. C. Greubel, Jul 28 2017
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CROSSREFS
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Cf. Fibonacci numbers A000045, tribonacci numbers A000213, tetranacci numbers A000288, pentanacci numbers A000322, hexanacci numbers A000383, 7th order Fibonacci numbers A060455, octanacci numbers.A123526, 9th order Fibonacci sequence A127193, 10th order Fibonacci sequence A127194.
Cf. A257966 (indices of primes in a), A257967 (primes in a).
Sequence in context: A064832 A129638 A333356 * A097616 A146150 A244069
Adjacent sequences: A127621 A127622 A127623 * A127625 A127626 A127627
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KEYWORD
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nonn,easy
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AUTHOR
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Luis A Restrepo (Luisiii(AT)mac.com), Jan 19 2007
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EXTENSIONS
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Edited by Dean Hickerson, Mar 09 2007
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STATUS
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approved
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