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%I #30 Feb 02 2021 22:43:35
%S 1,1,1,1,1,1,1,1,1,1,10,19,37,73,145,289,577,1153,2305,4609,9217,
%T 18424,36829,73621,147169,294193,588097,1175617,2350081,4697857,
%U 9391105,18772993,37527562,75018295,149962969,299778769,599263345,1197938593
%N A 10th-order Fibonacci sequence.
%C 10th-order Fibonacci constant = 1.999018633...
%H Robert Price, <a href="/A127194/b127194.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_10">Index entries for linear recurrences with constant coefficients</a>, signature (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) / (-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10). - _R. J. Mathar_, Nov 23 2007
%t With[{t=Table[1,{10}]},LinearRecurrence[t,t,40]] (* _Harvey P. Dale_, Nov 12 2013 *)
%o (PARI) a(n)=([0,1,0,0,0,0,0,0,0,0; 0,0,1,0,0,0,0,0,0,0; 0,0,0,1,0,0,0,0,0,0; 0,0,0,0,1,0,0,0,0,0; 0,0,0,0,0,1,0,0,0,0; 0,0,0,0,0,0,1,0,0,0; 0,0,0,0,0,0,0,1,0,0; 0,0,0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,0,0,1; 1,1,1,1,1,1,1,1,1,1]^(n-1)*[1;1;1;1;1;1;1;1;1;1])[1,1] \\ _Charles R Greathouse IV_, Jun 15 2015
%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.
%Y Cf. A257073, A257074.
%K nice,nonn,easy
%O 1,11
%A Luis A Restrepo (luisiii(AT)hotmail.com), Jan 11 2007
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