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.

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, -2, 14, 7, -14, 6, 2, 1, -4, -14, 6, -21, 0, 28, -28, -1, -2, -2, 2, 0, 6, 4, -28, -1, 48, -8, 0, -2, 8, 14, -22, 7, 20, -14, 40, 6, 8, 2, -14, 1, -2, -4, 60, -14

Offset

0,8

Links

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

Formula

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

a(2*(5*n+k)-1) = Sum_{j=0..k} (-1)^j * C(k,j) * a(n+k-j) for k=1..5.

Maple

a:= proc(n) option remember; local m, q, r;
      m:= (irem(n, 10, '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, 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 *)

Crossrefs

Cf. A005590, A229817, A229818, A229819, A229821, A229822, A229823, A229824, A229825.

Sequence in context: A195220 A119546 A173204 * A229821 A229822 A229823

Adjacent sequences: A229817 A229818 A229819 * A229821 A229822 A229823

Keyword

sign,eigen

Author

Alois P. Heinz, Sep 30 2013

Status

approved