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A127624 An 11th order Fibonacci sequence. a(n) = a(n-1) + ... + a(n-11). 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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.

LINKS

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).

FORMULA

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

MATHEMATICA

Module[{nn=11, lr}, lr=PadRight[{}, nn, 1]; LinearRecurrence[lr, lr, 20]] (* Harvey P. Dale, Feb 04 2015 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Luis A Restrepo (Luisiii(AT)mac.com), Jan 19 2007

EXTENSIONS

Edited by Dean Hickerson, Mar 09 2007

STATUS

approved

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Last modified December 4 23:44 EST 2020. Contains 338943 sequences. (Running on oeis4.)