A229659 9-section a(9n+k) gives k-th differences of a for k=0..8 with a(n)=0 for n<8 and a(8)=1.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -8, 0, 0, 0, 0, 0, 0, 1, -7, 28, 0, 0, 0, 0, 0, 1, -6, 21, -56, 0, 0, 0, 0, 1, -5, 15, -35, 70, 0, 0, 0, 1, -4, 10, -20, 35, -56, 0, 0, 1, -3, 6, -10, 15, -21, 28, 0, 1, -2, 3, -4, 5, -6, 7, -8, 1, -1, 1, -1

Offset: 0

Author

Alois P. Heinz, Sep 27 2013

Keywords

• sign
• look
• eigen

Links

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

Crossrefs

Cf. A005590, A229653, A229654, A229655, A229656, A229657, A229658, A229660.

Programs

Maple

a:= proc(n) option remember; local m, q;
      m:= irem(n, 9, 'q'); `if`(n<9, `if`(n=8, 1, 0),
      add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))
    end:
seq(a(n), n=0..100);

Formula

a(9*n+k) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=0..8.