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A127843 a(1) = 1, a(2) = ... = a(9) = 0, a(n) = a(n-9)+a(n-8) for n>9.

%I A127843 #24 Oct 08 2018 11:00:27
%S A127843 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,2,1,0,0,0,0,0,1,
%T A127843 3,3,1,0,0,0,0,1,4,6,4,1,0,0,0,1,5,10,10,5,1,0,0,1,6,15,20,15,6,1,0,1,
%U A127843 7,21,35,35,21,7,1,1,8,28,56,70,56,28,8,2,9
%N A127843 a(1) = 1, a(2) = ... = a(9) = 0, a(n) = a(n-9)+a(n-8) for n>9.
%C A127843 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 A127843 Apart from offset same as A017867. - _Georg Fischer_, Oct 07 2018
%D A127843 S. Suter, Binet-like formulas for recurrent sequences with characteristic equation x^k=x+1, preprint, 2007. [Apparently unpublished as of May 2016]
%H A127843 Colin Barker, <a href="/A127843/b127843.txt">Table of n, a(n) for n = 1..1000</a>
%H A127843 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,1).
%F A127843 Binet-like formula: a(n) = Sum_{i=1..9} (r_i^n)/(8(r_i)^2+9(r_i)) where r_i is a root of x^9=x+1.
%F A127843 G.f.: x*(1-x)*(1+x)*(1+x^2)*(1+x^4) / (1-x^8-x^9). - _Colin Barker_, May 30 2016
%t A127843 LinearRecurrence[{0,0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,0},120] (* _Harvey P. Dale_, Jun 15 2017 *)
%t A127843 CoefficientList[Series[(1-x)*(1+x)*(1+x^2)*(1+x^4) / (1-x^8-x^9), {x, 0, 50}], x] (* _Stefano Spezia_, Oct 08 2018 *)
%o A127843 (PARI) Vec(x*(1-x)*(1+x)*(1+x^2)*(1+x^4)/(1-x^8-x^9) + O(x^100)) \\ _Colin Barker_, May 30 2016
%o A127843 (GAP) a:=[1,0,0,0,0,0,0,0,0];;  for n in [10..90] do a[n]:=a[n-8]+a[n-9]; od; a; # _Muniru A Asiru_, Oct 07 2018
%K A127843 nonn,easy
%O A127843 1,27
%A A127843 Stephen Suter (sms5064(AT)psu.edu), Apr 02 2007