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A229820 Even bisection gives sequence a itself, n->a(2*(5*n+k)-1) gives k-th differences of a for k=1..5 with a(n)=n for n<2.

%I A229820 #11 Mar 08 2017 04:23:52
%S A229820 0,1,1,-1,1,-1,-1,7,1,-21,-1,0,-1,-2,7,6,1,-14,-21,28,-1,-2,0,4,-1,-8,
%T A229820 -2,14,7,-14,6,2,1,-4,-14,6,-21,0,28,-28,-1,-2,-2,2,0,6,4,-28,-1,48,
%U A229820 -8,0,-2,8,14,-22,7,20,-14,40,6,8,2,-14,1,-2,-4,60,-14
%N A229820 Even bisection gives sequence a itself, n->a(2*(5*n+k)-1) gives k-th differences of a for k=1..5 with a(n)=n for n<2.
%H A229820 Alois P. Heinz, <a href="/A229820/b229820.txt">Table of n, a(n) for n = 0..10000</a>
%F A229820 a(2*n) = a(n),
%F A229820 a(2*(5*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..5.
%p A229820 a:= proc(n) option remember; local m, q, r;
%p A229820       m:= (irem(n, 10, 'q')+1)/2;
%p A229820       `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
%p A229820       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
%p A229820     end:
%p A229820 seq(a(n), n=0..100);
%t A229820 a[n_] := a[n] = Module[{m, q, r, q2, r2}, {q, r} = QuotientRemainder[n, 10]; 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 A229820 Cf. A005590, A229817, A229818, A229819, A229821, A229822, A229823, A229824, A229825.
%K A229820 sign,eigen
%O A229820 0,8
%A A229820 _Alois P. Heinz_, Sep 30 2013