A229659 - OEIS

%I #8 Jan 26 2014 17:13:05

%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,-8,0,0,0,0,0,0,1,-7,28,0,0,0,0,0,1,

%T -6,21,-56,0,0,0,0,1,-5,15,-35,70,0,0,0,1,-4,10,-20,35,-56,0,0,1,-3,6,

%U -10,15,-21,28,0,1,-2,3,-4,5,-6,7,-8,1,-1,1,-1

%N 9-section a(9n+k) gives k-th differences of a for k=0..8 with a(n)=0 for n<8 and a(8)=1.

%H Alois P. Heinz, <a href="/A229659/b229659.txt">Table of n, a(n) for n = 0..10000</a>

%F a(9*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..8.

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

%p       m:= irem(n, 9, 'q'); `if`(n<9, `if`(n=8, 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, A229658, A229660.

%K sign,look,eigen

%O 0,18

%A _Alois P. Heinz_, Sep 27 2013