|
%I #34 Jan 31 2021 21:00:42
%S 1,1,1,1,1,1,1,1,1,1,1,11,21,41,81,161,321,641,1281,2561,5121,10241,
%T 20481,40951,81881,163721,327361,654561,1308801,2616961,5232641,
%U 10462721,20920321,41830401,83640321,167239691,334397501,668631281
%N An 11th-order Fibonacci sequence: a(n) = a(n-1) + ... + a(n-11).
%C The ratio a(n+1)/a(n) approaches the unique real root of r^11 = r^10 + ... + r + 1; r is about 1.99951040197828549144.
%C All terms have last digit 1.
%H Robert Price, <a href="/A127624/b127624.txt">Table of n, a(n) for n = 1..1000</a>
%H E. S. Croot, <a href="http://people.math.gatech.edu/~ecroot/recurrence_notes2.pdf">Notes on Linear Recurrence Sequences</a>
%H M. A. Lerma, <a href="http://www.math.northwestern.edu/~mlerma/problem_solving/results/recurrences.pdf">Recurrence Relations</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1,1,1).
%F 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
%t Module[{nn=11,lr},lr=PadRight[{},nn,1];LinearRecurrence[lr,lr,20]] (* _Harvey P. Dale_, Feb 04 2015 *)
%o (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
%Y 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.
%Y Cf. A257966 (indices of primes in a), A257967 (primes in a).
%K nonn,easy
%O 1,12
%A Luis A Restrepo (Luisiii(AT)mac.com), Jan 19 2007
%E Edited by _Dean Hickerson_, Mar 09 2007
|
