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%I #10 Mar 08 2017 03:57:09
%S 0,1,1,-1,1,-1,-1,0,1,-2,-1,6,-1,-2,0,4,1,-8,-2,2,-1,-4,6,6,-1,-2,-2,
%T 2,0,-1,4,0,1,1,-8,-1,-2,1,2,0,-1,-4,-4,1,6,-4,6,8,-1,-3,-2,4,-2,2,2,
%U 1,0,6,-1,-20,4,7,0,-14,1,20,1,-7,-8,6,-1,-3,-2,-1
%N Even bisection gives sequence a itself, n->a(2*(3*n+k)-1) gives k-th differences of a for k=1..3 with a(n)=n for n<2.
%H Alois P. Heinz, <a href="/A229818/b229818.txt">Table of n, a(n) for n = 0..10000</a>
%F a(2*n) = a(n),
%F a(6*n+1) = a(n+1) - a(n),
%F a(6*n+3) = a(n+2) - 2*a(n+1) + a(n),
%F a(6*n+5) = a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n).
%p a:= proc(n) option remember; local m, q, r;
%p m:= (irem(n, 6, 'q')+1)/2;
%p `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
%p add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
%p end:
%p seq(a(n), n=0..100);
%t a[n_] := a[n] = Module[{m, q, r, q2, r2}, {q, r} = QuotientRemainder[n, 6]; m = (r+1)/2; If[n<2, n, {q2, r2} = QuotientRemainder[n, 2]; If[r2 == 0, a[q2], Sum[a[q+m-j]*(-1)^j*Binomial[m, j], {j, 0, m}]]]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Mar 08 2017, translated from Maple *)
%Y Cf. A005590, A229817, A229819, A229820, A229821, A229822, A229823, A229824, A229825.
%K sign,eigen
%O 0,10
%A _Alois P. Heinz_, Sep 30 2013
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