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A306758 a(n) = a(n-9) + a(n-10) with a(0)=10, a(1)=...=a(8)=0, a(9)=9.

%I A306758 #14 Jan 18 2021 15:25:33
%S A306758 10,0,0,0,0,0,0,0,0,9,10,0,0,0,0,0,0,0,9,19,10,0,0,0,0,0,0,9,28,29,10,
%T A306758 0,0,0,0,0,9,37,57,39,10,0,0,0,0,9,46,94,96,49,10,0,0,0,9,55,140,190,
%U A306758 145,59,10,0,0,9,64,195,330,335,204,69,10,0,9,73,259,525,665
%N A306758 a(n) = a(n-9) + a(n-10) with a(0)=10, a(1)=...=a(8)=0, a(9)=9.
%C A306758 Conjecture: If p is prime, p divides a(p).
%H A306758 Seiichi Manyama, <a href="/A306758/b306758.txt">Table of n, a(n) for n = 0..10000</a>
%H A306758 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1,1).
%F A306758 G.f.: (10 - x^9)/(1 - x^9 - x^10).
%F A306758 a(0) = 10 and a(n) = n*Sum_{k=1..floor(n/9)} binomial(k,n-9*k)/k for n > 0.
%t A306758 LinearRecurrence[{0,0,0,0,0,0,0,0,1,1},{10,0,0,0,0,0,0,0,0,9},80] (* _Harvey P. Dale_, Jan 18 2021 *)
%o A306758 (PARI) N=99; x='x+O('x^N); Vec((10-x^9)/(1-x^9-x^10))
%Y A306758 Column 9 of A306646.
%K A306758 nonn,easy
%O A306758 0,1
%A A306758 _Seiichi Manyama_, Mar 08 2019