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A306755 a(n) = a(n-6) + a(n-7) with a(0)=7, a(1)=...=a(5)=0, a(6)=6.

%I A306755 #24 Dec 19 2022 17:31:41
%S A306755 7,0,0,0,0,0,6,7,0,0,0,0,6,13,7,0,0,0,6,19,20,7,0,0,6,25,39,27,7,0,6,
%T A306755 31,64,66,34,7,6,37,95,130,100,41,13,43,132,225,230,141,54,56,175,357,
%U A306755 455,371,195,110,231,532,812,826,566,305,341,763,1344,1638,1392,871,646,1104,2107
%N A306755 a(n) = a(n-6) + a(n-7) with a(0)=7, a(1)=...=a(5)=0, a(6)=6.
%C A306755 Conjecture: If p is prime, p divides a(p).
%H A306755 Seiichi Manyama, <a href="/A306755/b306755.txt">Table of n, a(n) for n = 0..10000</a>
%H A306755 Johann Cigler, <a href="https://arxiv.org/abs/2212.02118">Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials</a>, arXiv:2212.02118 [math.NT], 2022.
%H A306755 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1,1).
%F A306755 G.f.: (7 - x^6)/(1 - x^6 - x^7).
%F A306755 a(0) = 7 and a(n) = n*Sum_{k=1..floor(n/6)} binomial(k,n-6*k)/k for n > 0.
%t A306755 LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {7, 0, 0, 0, 0, 0, 6}, 100] (* _Amiram Eldar_, Jun 21 2021 *)
%o A306755 (PARI) N=66; x='x+O('x^N); Vec((7-x^6)/(1-x^6-x^7))
%Y A306755 Column 6 of A306646.
%K A306755 nonn,easy
%O A306755 0,1
%A A306755 _Seiichi Manyama_, Mar 08 2019