cp's OEIS Frontend

A229819 Even bisection gives sequence a itself, n->a(2*(4*n+k)-1) gives k-th differences of a for k=1..4 with a(n)=n for n<2.

%I A229819 #12 Mar 08 2017 04:23:24
%S A229819 0,1,1,-1,1,-1,-1,7,1,0,-1,-2,-1,6,7,-14,1,-2,0,4,-1,-8,-2,14,-1,2,6,
%T A229819 -4,7,6,-14,0,1,-2,-2,2,0,6,4,-28,-1,0,-8,8,-2,-22,14,41,-1,8,2,-14,6,
%U A229819 19,-4,-24,7,-6,6,5,-14,-5,0,5,1,-1,-2,0,-2,0,2,2,0
%N A229819 Even bisection gives sequence a itself, n->a(2*(4*n+k)-1) gives k-th differences of a for k=1..4 with a(n)=n for n<2.
%H A229819 Alois P. Heinz, <a href="/A229819/b229819.txt">Table of n, a(n) for n = 0..10000</a>
%F A229819 a(2*n)   = a(n),
%F A229819 a(8*n+1) = a(n+1) - a(n),
%F A229819 a(8*n+3) = a(n+2) - 2*a(n+1) + a(n),
%F A229819 a(8*n+5) = a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n).
%F A229819 a(8*n+7) = a(n+4) - 4*a(n+3) + 6*a(n+2) - 4*a(n+1) + a(n).
%p A229819 a:= proc(n) option remember; local m, q, r;
%p A229819       m:= (irem(n, 8, 'q')+1)/2;
%p A229819       `if`(n<2, n, `if`(irem(n, 2, 'r')=0, a(r),
%p A229819       add(a(q+m-j)*(-1)^j*binomial(m, j), j=0..m)))
%p A229819     end:
%p A229819 seq(a(n), n=0..100);
%t A229819 a[n_] := a[n] = Module[{m, q, r, q2, r2}, {q, r} = QuotientRemainder[n, 8]; 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 *)
%Y A229819 Cf. A005590, A229817, A229818, A229820, A229821, A229822, A229823, A229824, A229825.
%K A229819 sign,eigen
%O A229819 0,8
%A A229819 _Alois P. Heinz_, Sep 30 2013