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

Author

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

Keywords

• nonn
• easy

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).

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).

Programs

Mathematica

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

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

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

Extensions

Edited by Dean Hickerson, Mar 09 2007