A229817 Even bisection gives sequence a itself, n->a(2*(2*n+k)-1) gives k-th differences of a for k=1..2 with a(n)=n for n<2.

0, 1, 1, -1, 1, 0, -1, -2, 1, -2, 0, 4, -1, 2, -2, -3, 1, -1, -2, 0, 0, -1, 4, 0, -1, -1, 2, 4, -2, 3, -3, -6, 1, -3, -1, 5, -2, 2, 0, 2, 0, 4, -1, -9, 4, -5, 0, 8, -1, 3, -1, -7, 2, -4, 4, 3, -2, -1, 3, 5, -3, 4, -6, -6, 1, -2, -3, 1, -1, -1, 5, 3, -2, 2, 2

Offset: 0

Author

Alois P. Heinz, Sep 30 2013

Keywords

• sign
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005590, A229818, A229819, A229820, A229821, A229822, A229823, A229824, A229825.

Programs

Maple

a:= proc(n) option remember; local m, q, r;
      m:= (irem(n, 4, 'q')+1)/2;
      `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
      add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
    end:
seq(a(n), n=0..100);

Mathematica

a[n_] := a[n] = Module[{m, q, r}, {q, m} = QuotientRemainder[n, 4]; m = (m + 1)/2; If[n<2, n, If[Mod[n, 2]==0, a[Quotient[n, 2]], Sum[a[q+m-j] * (-1)^j * Binomial[m, j], {j, 0, m}]]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 22 2017, translated from Maple *)

Formula

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

a(4*n+1) = a(n+1) - a(n),

a(4*n+3) = a(n+2) - 2*a(n+1) + a(n).