A127624 An 11th-order Fibonacci sequence: a(n) = a(n-1) + ... + a(n-11).

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

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, 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

Keyword

nonn,easy

Author

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

Extensions

Edited by Dean Hickerson, Mar 09 2007

Status

approved