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A229823 Even bisection gives sequence a itself, n->a(2*(8*n+k)-1) gives k-th differences of a for k=1..8 with a(n)=n for n<2.

%I A229823 #9 Mar 08 2017 04:25:48
%S A229823 0,1,1,-1,1,-1,-1,7,1,-21,-1,49,-1,-91,7,119,1,0,-21,-2,-1,6,49,-14,
%T A229823 -1,28,-91,-42,7,28,119,62,1,-2,0,4,-21,-8,-2,14,-1,-14,6,-14,49,90,
%U A229823 -14,-174,-1,2,28,-4,-91,6,-42,0,7,-28,28,76,119,-84,62,-78,1
%N A229823 Even bisection gives sequence a itself, n->a(2*(8*n+k)-1) gives k-th differences of a for k=1..8 with a(n)=n for n<2.
%H A229823 Alois P. Heinz, <a href="/A229823/b229823.txt">Table of n, a(n) for n = 0..10000</a>
%F A229823 a(2*n) = a(n),
%F A229823 a(2*(8*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..8.
%p A229823 a:= proc(n) option remember; local m, q, r;
%p A229823       m:= (irem(n, 16, 'q')+1)/2;
%p A229823       `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
%p A229823       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
%p A229823     end:
%p A229823 seq(a(n), n=0..100);
%t A229823 a[n_] := a[n] = Module[{m, q, r, q2, r2}, {q, r} = QuotientRemainder[n, 16]; 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 A229823 Cf. A005590, A229817, A229818, A229819, A229820, A229821, A229822, A229824, A229825.
%K A229823 sign,eigen
%O A229823 0,8
%A A229823 _Alois P. Heinz_, Sep 30 2013