A229825 Even bisection gives sequence a itself, n->a(2*(10*n+k)-1) gives k-th differences of a for k=1..10 with a(n)=n for n<2.

0, 1, 1, -1, 1, -1, -1, 7, 1, -21, -1, 49, -1, -91, 7, 119, 1, -57, -21, -179, -1, 0, 49, -2, -1, 6, -91, -14, 7, 28, 119, -42, 1, 28, -57, 62, -21, -236, -179, 332, -1, -2, 0, 4, 49, -8, -2, 14, -1, -14, 6, -14, -91, 90, -14, -174, 7, 96, 28, 396, 119, 2, -42

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, A229817, A229818, A229819, A229820, A229821, A229822, A229823, A229824.

Programs

Maple

a:= proc(n) option remember; local m, q, r;
      m:= (irem(n, 20, '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, q2, r2}, {q, r} = QuotientRemainder[n, 20]; 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 *)

Formula

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

a(2*(10*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..10.