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A123526 Octanacci numbers.

%I A123526 #30 Mar 10 2021 18:19:13
%S A123526 1,1,1,1,1,1,1,1,8,15,29,57,113,225,449,897,1793,3578,7141,14253,
%T A123526 28449,56785,113345,226241,451585,901377,1799176,3591211,7168169,
%U A123526 14307889,28558993,57004641,113783041,227114497,453327617,904856058,1806120905
%N A123526 Octanacci numbers.
%H A123526 Robert Price, <a href="/A123526/b123526.txt">Table of n, a(n) for n = 1..1000</a>
%H A123526 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1,1).
%F A123526 a(n)=1 for 1 <= n <= 8, a(n) = a(n-1) + a(n-2) +...+ a(n-8) for n > 8.
%F A123526 G.f.: x*(1 -x^2 -2*x^3 -3*x^4 -4*x^5 -5*x^6 -6*x^7)/(1 -x -x^2 -x^3 -x^4 -x^5 -x^6 -x^7 -x^8). - _Colin Barker_, Oct 19 2015
%p A123526 m:=50; S:=series( x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8), x, m+1):
%p A123526 seq(coeff(S, x, j), j=1..m); # _G. C. Greubel_, Mar 10 2021
%t A123526 Module[{nn=8,lr},lr=PadRight[{},nn,1];LinearRecurrence[lr,lr,20]] (* _Harvey P. Dale_, Feb 04 2015 *)
%o A123526 (PARI) Vec(x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8) + O(x^50)) \\ _Colin Barker_, Oct 19 2015
%o A123526 (Sage)
%o A123526 @CachedFunction
%o A123526 def A123526(n):
%o A123526     if (n<9): return 1
%o A123526     else: return sum(A(n-j) for j in (1..8))
%o A123526 [A123526(n) for n in [1..50]] # _G. C. Greubel_, Mar 10 2021
%o A123526 (Magma)
%o A123526 R<x>:=PowerSeriesRing(Integers(), 50);
%o A123526 Coefficients(R!( x*(1-x^2-2*x^3-3*x^4-4*x^5-5*x^6-6*x^7)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8) )); // _G. C. Greubel_, Mar 10 2021
%Y A123526 Cf. A000045, A000213, A000288, A000322, A000383, A060455, A079262.
%Y A123526 Cf. A254412, A254413.  Indices of primes and primes in this sequence.
%K A123526 easy,nonn
%O A123526 1,9
%A A123526 _Danny Rorabaugh_, Nov 10 2006