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A229821 Even bisection gives sequence a itself, n->a(2*(6*n+k)-1) gives k-th differences of a for k=1..6 with a(n)=n for n<2.

%I A229821 #9 Mar 08 2017 04:24:55
%S A229821 0,1,1,-1,1,-1,-1,7,1,-21,-1,49,-1,0,7,-2,1,6,-21,-14,-1,28,49,-42,-1,
%T A229821 -2,0,4,7,-8,-2,14,1,-14,6,-14,-21,2,-14,-4,-1,6,28,0,49,-28,-42,76,
%U A229821 -1,-2,-2,2,0,6,4,-28,7,48,-8,-8,-2,0,14,8,1,-22,-14,20,6
%N A229821 Even bisection gives sequence a itself, n->a(2*(6*n+k)-1) gives k-th differences of a for k=1..6 with a(n)=n for n<2.
%H A229821 Alois P. Heinz, <a href="/A229821/b229821.txt">Table of n, a(n) for n = 0..10000</a>
%F A229821 a(2*n) = a(n),
%F A229821 a(2*(6*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..6.
%p A229821 a:= proc(n) option remember; local m, q, r;
%p A229821       m:= (irem(n, 12, 'q')+1)/2;
%p A229821       `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
%p A229821       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
%p A229821     end:
%p A229821 seq(a(n), n=0..100);
%t A229821 a[n_] := a[n] = Module[{m, q, r, q2, r2}, {q, r} = QuotientRemainder[n, 12]; 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 A229821 Cf. A005590, A229817, A229818, A229819, A229820, A229822, A229823, A229824, A229825.
%K A229821 sign,eigen
%O A229821 0,8
%A A229821 _Alois P. Heinz_, Sep 30 2013