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A229657 7-section a(7n+k) gives k-th differences of a for k=0..6 with a(n)=0 for n<6 and a(6)=1.

%I A229657 #8 Jan 27 2014 11:19:59
%S A229657 0,0,0,0,0,0,1,0,0,0,0,0,1,-6,0,0,0,0,1,-5,15,0,0,0,1,-4,10,-20,0,0,1,
%T A229657 -3,6,-10,15,0,1,-2,3,-4,5,-6,1,-1,1,-1,1,-1,2,0,0,0,0,0,1,-12,0,0,0,
%U A229657 0,1,-11,51,0,0,0,1,-10,40,-110,0,0,1,-9,30,-70
%N A229657 7-section a(7n+k) gives k-th differences of a for k=0..6 with a(n)=0 for n<6 and a(6)=1.
%H A229657 Alois P. Heinz, <a href="/A229657/b229657.txt">Table of n, a(n) for n = 0..10000</a>
%F A229657 a(7*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..6.
%p A229657 a:= proc(n) option remember; local m, q;
%p A229657       m:= irem(n, 7, 'q'); `if`(n<7, `if`(n=6, 1, 0),
%p A229657       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))
%p A229657     end:
%p A229657 seq(a(n), n=0..100);
%Y A229657 Cf. A005590, A229653, A229654, A229655, A229656, A229658, A229659, A229660.
%K A229657 sign,eigen,look
%O A229657 0,14
%A A229657 _Alois P. Heinz_, Sep 27 2013