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A229653 Trisection a(3n+k) gives k-th differences of a for k=0..2 with a(n)=0 for n<2 and a(2)=1. 8
0, 0, 1, 0, 1, -2, 1, -1, 2, 0, 1, -4, 1, -3, 6, -2, 3, -5, 1, -2, 5, -1, 3, -5, 2, -2, 3, 0, 1, -6, 1, -5, 10, -4, 5, -9, 1, -4, 13, -3, 9, -17, 6, -8, 13, -2, 5, -13, 3, -8, 14, -5, 6, -9, 1, -3, 10, -2, 7, -13, 5, -6, 10, -1, 4, -12, 3, -8, 15, -5, 7, -11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..19683

FORMULA

a(3*n)   = a(n),

a(3*n+1) = a(n+1) - a(n),

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

MAPLE

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

      m:= irem(n, 3, 'q'); `if`(n<3, `if`(n=2, 1, 0),

      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}, {q, m} = QuotientRemainder[n, 3]; If[n < 3, If[n == 2, 1, 0], Sum[a[q + m - j]*(-1)^j*Binomial[m, j], {j, 0, m}]]];

Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Jun 09 2018, translated from Maple *)

CROSSREFS

Cf. A005590, A229654, A229655, A229656, A229657, A229658, A229659, A229660.

Sequence in context: A096496 A117209 A035192 * A089062 A282634 A039980

Adjacent sequences:  A229650 A229651 A229652 * A229654 A229655 A229656

KEYWORD

sign,eigen,look

AUTHOR

Alois P. Heinz, Sep 27 2013

STATUS

approved

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Last modified November 15 10:31 EST 2018. Contains 317237 sequences. (Running on oeis4.)