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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, heptanacci 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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