|
%I #31 Nov 20 2020 07:17:39
%S 1,1,1,1,1,1,1,1,1,9,17,33,65,129,257,513,1025,2049,4097,8185,16353,
%T 32673,65281,130433,260609,520705,1040385,2078721,4153345,8298505,
%U 16580657,33128641,66192001,132253569,264246529,527972353,1054904321
%N A 9th-order Fibonacci sequence.
%C 9-Bonacci constant = 1.99802947...
%H Robert Price, <a href="/A127193/b127193.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_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1,1).
%F For a(1)=...=a(9)=1, a(10)=9, a(n)= 2*a(n-1) - a(n-10). - _Vincenzo Librandi_, Dec 20 2010
%F G.f.: x*(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8+7*x^9)/(1-2*x+x^10). - _G. C. Greubel_, Jul 28 2017
%t LinearRecurrence[{1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,1,1},40] (* _Ray Chandler_, Aug 01 2015 *)
%t With[{c=Table[1,{9}]},LinearRecurrence[c,c,40]] (* _Harvey P. Dale_, Apr 08 2016 *)
%o (PARI) x='x+O('x^50); Vec((x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9+7*x^10)/(1 -2*x+ x^10)) \\ _G. C. Greubel_, Jul 28 2017
%Y Cf. Fibonacci numbers A000045, tribonacci numbers A000213, tetranacci numbers A000288, pentanacci numbers A000322, hexanacci numbers A000383, 7th-order Fibonacci numbers A060455, octanacci numbers, A123526.
%K nonn,easy
%O 1,10
%A Luis A Restrepo (luisiii(AT)mac.com), Jan 07 2007
|
