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%I #23 Oct 08 2018 05:56:52
%S 1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,2,1,0,0,0,
%T 0,0,0,1,3,3,1,0,0,0,0,0,1,4,6,4,1,0,0,0,0,1,5,10,10,5,1,0,0,0,1,6,15,
%U 20,15,6,1,0,0,1,7,21,35,35,21,7,1,0,1,8,28
%N a(1) = 1, a(2) = ... = a(10) = 0, a(n) = a(n-10)+a(n-9) for n>10.
%C Part of the phi_k family of sequences defined by a(1)=1,a(2)=...=a(k)=0, a(n)=a(n-k)+a(n-k+1) for n>k. phi_2 is a shift of the Fibonacci sequence and phi_3 is a shift of the Padovan sequence.
%C Apart from offset same as A017877. - _Georg Fischer_, Oct 07 2018
%D S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007. [Apparently unpublished as of May 2016]
%H Colin Barker, <a href="/A127844/b127844.txt">Table of n, a(n) for n = 1..1000</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 Binet-like formula: a(n) = Sum_{i=1..10} (r_i^n)/(9(r_i)^2+10(r_i)) where r_i is a root of x^10=x+1.
%F G.f.: x*(1-x)*(1+x+x^2)*(1+x^3+x^6) / (1-x^9-x^10). - _Colin Barker_, May 30 2016
%t LinearRecurrence[{0,0,0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,0,0},100] (* _Harvey P. Dale_, Jun 18 2017 *)
%o (PARI) Vec(x*(1-x)*(1+x+x^2)*(1+x^3+x^6)/(1-x^9-x^10) + O(x^100)) \\ _Colin Barker_, May 30 2016
%o (GAP) a:=[1,0,0,0,0,0,0,0,0,0];; for n in [11..90] do a[n]:=a[n-9]+a[n-10]; od; a; # _Muniru A Asiru_, Oct 07 2018
%K nonn,easy
%O 1,30
%A Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007
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