A229823 - OEIS

%I #9 Mar 08 2017 04:25:48

%S 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 -1,28,-91,-42,7,28,119,62,1,-2,0,4,-21,-8,-2,14,-1,-14,6,-14,49,90,

%U -14,-174,-1,2,28,-4,-91,6,-42,0,7,-28,28,76,119,-84,62,-78,1

%N 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 Alois P. Heinz, <a href="/A229823/b229823.txt">Table of n, a(n) for n = 0..10000</a>

%F a(2*n) = a(n),

%F a(2*(8*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..8.

%p a:= proc(n) option remember; local m, q, r;

%p       m:= (irem(n, 16, '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, 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 Cf. A005590, A229817, A229818, A229819, A229820, A229821, A229822, A229824, A229825.

%K sign,eigen

%O 0,8

%A _Alois P. Heinz_, Sep 30 2013