A229653 - OEIS

%I #20 Jun 16 2018 18:51:54

%S 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,

%T -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,

%U 1,-3,10,-2,7,-13,5,-6,10,-1,4,-12,3,-8,15,-5,7,-11

%N 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.

%H Alois P. Heinz, <a href="/A229653/b229653.txt">Table of n, a(n) for n = 0..19683</a>

%F a(3*n)   = a(n),

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

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

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

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

%p       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m))

%p     end:

%p seq(a(n), n=0..100);

%t 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}]]];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jun 09 2018, translated from Maple *)

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

%K sign,eigen,look

%O 0,6

%A _Alois P. Heinz_, Sep 27 2013