A119583 a(1)=0, a(2)=0, a(3)=0, a(4)=1 then a(n)=abs(a(n-1)-2*a(n-2)+a(n-3))-a(n-4).

0, 0, 0, 1, 1, 1, 0, 0, 0, -1, 1, 3, 0, 6, 8, 1, 9, 9, 0, 8, 8, -1, 9, 11, 0, 14, 16, 1, 17, 17, 0, 16, 16, -1, 17, 19, 0, 22, 24, 1, 25, 25, 0, 24, 24, -1, 25, 27, 0, 30, 32, 1, 33, 33, 0, 32, 32, -1, 33, 35, 0, 38, 40, 1, 41, 41, 0, 40, 40, -1, 41, 43, 0, 46, 48, 1, 49, 49, 0, 48, 48, -1, 49, 51, 0, 54, 56, 1, 57, 57, 0, 56, 56, -1, 57, 59, 0, 62, 64

Offset

1,12

References

B. Cloitre, On strange predictible recursions, preprint 2006

Links

Table of n, a(n) for n=1..99.

Formula

for n>=1 : a(6*n)=4*n-4-(-1)^n, a(6n+1)=0, a(6*n+2)=4*n-3+(-1)^n, a(6*n+3)=4*n-2+2*(-1)^n, a(6*n+4)=(-1)^n, a(6*n+5)=4*n-1+2*(-1)^n.

Empirical g.f.: x^4*(2*x^10+5*x^8+3*x^7+x^6-2*x^5-2*x^4-2*x^3+x^2+x+1) / (x^12-2*x^9+2*x^6-2*x^3+1). - Colin Barker, Jun 28 2013

Mathematica

RecurrenceTable[{a[1]==a[2]==a[3]==0, a[4]==1, a[n]==Abs[a[n-1]-2a[n-2]+ a[n-3]]- a[n-4]}, a, {n, 100}] (* Harvey P. Dale, Mar 13 2014 *)

Crossrefs

Cf. A104156, A119557, A119558.

Sequence in context: A021330 A199055 A016598 * A309604 A244009 A321482

Adjacent sequences: A119580 A119581 A119582 * A119584 A119585 A119586

Keyword

sign

Author

Benoit Cloitre, May 31 2006

Status

approved