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a(n) = a(n-9) + a(n-10) with a(0)=10, a(1)=...=a(8)=0, a(9)=9.
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%I #14 Jan 18 2021 15:25:33

%S 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 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 145,59,10,0,0,9,64,195,330,335,204,69,10,0,9,73,259,525,665

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

%C Conjecture: If p is prime, p divides a(p).

%H Seiichi Manyama, <a href="/A306758/b306758.txt">Table of n, a(n) for n = 0..10000</a>

%H <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 G.f.: (10 - x^9)/(1 - x^9 - x^10).

%F a(0) = 10 and a(n) = n*Sum_{k=1..floor(n/9)} binomial(k,n-9*k)/k for n > 0.

%t 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 (PARI) N=99; x='x+O('x^N); Vec((10-x^9)/(1-x^9-x^10))

%Y Column 9 of A306646.

%K nonn,easy

%O 0,1

%A _Seiichi Manyama_, Mar 08 2019