A078113 Let u(1)=u(2)=1, u(3)=n, u(k) = (1/2)*abs(2*u(k-1) -u(k-2)-u(k-3)); sequence gives values of n such that sum(k>=1, u(k)) is an integer.

2, 6, 7, 15, 17, 33, 37, 69, 77, 141, 157, 285, 317, 573, 637, 1149, 1277, 2301, 2557, 4605, 5117, 9213, 10237, 18429, 20477, 36861, 40957, 73725, 81917, 147453, 163837, 294909, 327677

Offset

1,1

Comments

u(3)=7, sum(k>=1,u(k)) = 28 is an integer, hence 7 is in the sequence.

Links

Table of n, a(n) for n=1..33.

Formula

Conjecture: a(n) = -3+2^(1/2*(-5+n))*(10-10*(-1)^n+9*sqrt(2)+9*(-1)^n*sqrt(2)). a(n) = a(n-1)+2*a(n-2)-2*a(n-3). G.f.: x*(3*x^2-4*x-2) / ((x-1)*(2*x^2-1)). - Colin Barker, Aug 14 2013

Prog

(PARI)
A078113(maxn, maxk) = {
  u=vector(maxk);
  u[1]=1; u[2]=1;
  for(n=1, maxn,
    u[3]=n;
    for(k=4, maxk, u[k]=abs(2*u[k-1]-u[k-2]-u[k-3])/2);
    s=sum(i=1, maxk, u[i]);
    if(ceil(s)-s < 1E-11, print1(n, ", ")) \\ Arbitrary 1E-11
  )
}
A078113(1000000, 200) \\ Colin Barker, Aug 14 2013

Crossrefs

Sequence in context: A344343 A226965 A128918 * A286054 A340376 A030607

Adjacent sequences: A078110 A078111 A078112 * A078114 A078115 A078116

Keyword

nonn,more

Author

Benoit Cloitre, Dec 04 2002

Extensions

More terms from Colin Barker, Aug 14 2013

Status

approved