A229658 - OEIS

%I #9 Jan 27 2014 11:20:39

%S 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 -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 -1,1,-1,1,-1,1,0,0,0,0,0,0,0,1,-14,0,0,0,0,0,1

%N 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 Alois P. Heinz, <a href="/A229658/b229658.txt">Table of n, a(n) for n = 0..10000</a>

%F a(8*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..7.

%p a:= proc(n) option remember; local m, q;

%p       m:= irem(n, 8, 'q'); `if`(n<8, `if`(n=7, 1, 0),

%p       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))

%p     end:

%p seq(a(n), n=0..100);

%Y Cf. A005590, A229653, A229654, A229655, A229656, A229657, A229659, A229660.

%K sign,eigen,look

%O 0,16

%A _Alois P. Heinz_, Sep 27 2013