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A229658 8-section a(8n+k) gives k-th differences of a for k=0..7 with a(n)=0 for n<7 and a(7)=1.

%I A229658 #9 Jan 27 2014 11:20:39
%S A229658 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,-7,0,0,0,0,0,1,-6,21,0,0,0,0,1,-5,15,
%T A229658 -35,0,0,0,1,-4,10,-20,35,0,0,1,-3,6,-10,15,-21,0,1,-2,3,-4,5,-6,7,1,
%U A229658 -1,1,-1,1,-1,1,0,0,0,0,0,0,0,1,-14,0,0,0,0,0,1
%N A229658 8-section a(8n+k) gives k-th differences of a for k=0..7 with a(n)=0 for n<7 and a(7)=1.
%H A229658 Alois P. Heinz, <a href="/A229658/b229658.txt">Table of n, a(n) for n = 0..10000</a>
%F A229658 a(8*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..7.
%p A229658 a:= proc(n) option remember; local m, q;
%p A229658       m:= irem(n, 8, 'q'); `if`(n<8, `if`(n=7, 1, 0),
%p A229658       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))
%p A229658     end:
%p A229658 seq(a(n), n=0..100);
%Y A229658 Cf. A005590, A229653, A229654, A229655, A229656, A229657, A229659, A229660.
%K A229658 sign,eigen,look
%O A229658 0,16
%A A229658 _Alois P. Heinz_, Sep 27 2013