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A306756 a(n) = a(n-7) + a(n-8) with a(0)=8, a(1)=...=a(6)=0, a(7)=7.

%I A306756 #17 Jun 21 2021 03:01:29
%S A306756 8,0,0,0,0,0,0,7,8,0,0,0,0,0,7,15,8,0,0,0,0,7,22,23,8,0,0,0,7,29,45,
%T A306756 31,8,0,0,7,36,74,76,39,8,0,7,43,110,150,115,47,8,7,50,153,260,265,
%U A306756 162,55,15,57,203,413,525,427,217,70,72,260,616,938,952,644,287,142
%N A306756 a(n) = a(n-7) + a(n-8) with a(0)=8, a(1)=...=a(6)=0, a(7)=7.
%C A306756 Conjecture: If p is prime, p divides a(p).
%H A306756 Seiichi Manyama, <a href="/A306756/b306756.txt">Table of n, a(n) for n = 0..10000</a>
%H A306756 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1,1).
%F A306756 G.f.: (8 - x^7)/(1 - x^7 - x^8).
%F A306756 a(0) = 8 and a(n) = n*Sum_{k=1..floor(n/7)} binomial(k,n-7*k)/k for n > 0.
%t A306756 LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1}, {8, 0, 0, 0, 0, 0, 0, 7}, 100] (* _Amiram Eldar_, Jun 21 2021 *)
%o A306756 (PARI) N=66; x='x+O('x^N); Vec((8-x^7)/(1-x^7-x^8))
%Y A306756 Column 7 of A306646.
%K A306756 nonn,easy
%O A306756 0,1
%A A306756 _Seiichi Manyama_, Mar 08 2019