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A229656 6-section a(6n+k) gives k-th differences of a for k=0..5 with a(n)=0 for n<5 and a(5)=1.

%I A229656 #10 Jan 27 2014 11:19:20
%S A229656 0,0,0,0,0,1,0,0,0,0,1,-5,0,0,0,1,-4,10,0,0,1,-3,6,-10,0,1,-2,3,-4,5,
%T A229656 1,-1,1,-1,1,0,0,0,0,0,1,-10,0,0,0,1,-9,35,0,0,1,-8,26,-60,0,1,-7,18,
%U A229656 -34,55,1,-6,11,-16,21,-25,-5,5,-5,5,-4,-4,0,0,0,1
%N A229656 6-section a(6n+k) gives k-th differences of a for k=0..5 with a(n)=0 for n<5 and a(5)=1.
%H A229656 Alois P. Heinz, <a href="/A229656/b229656.txt">Table of n, a(n) for n = 0..10000</a>
%F A229656 a(6*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..5.
%p A229656 a:= proc(n) option remember; local m, q;
%p A229656       m:= irem(n, 6, 'q'); `if`(n<6, `if`(n=5, 1, 0),
%p A229656       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))
%p A229656     end:
%p A229656 seq(a(n), n=0..100);
%Y A229656 Cf. A005590, A229653, A229654, A229655, A229657, A229658, A229659, A229660.
%K A229656 sign,eigen,look
%O A229656 0,12
%A A229656 _Alois P. Heinz_, Sep 27 2013