login
A130848
Periodic sequence with period (2, 5, 3, -2, -5, -3).
1
2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3, 2, 5, 3, -2, -5, -3
OFFSET
0,1
COMMENTS
Also binomial transform of periodic sequence with period (2, 3, -5).
Sequence is identical to its third differences.
FORMULA
For n > 1, a(n) = a(n-1) - a(n-2).
a(n) = a(n-6).
G.f.: (2+3*x)/(1-x+x^2).
a(n) = 2*cos(Pi*n/3) + (8/3)*3^(1/2)*sin(Pi*n/3). - R. J. Mathar, Nov 15 2007
MATHEMATICA
LinearRecurrence[{1, -1}, {2, 5}, 120] (* or *) PadRight[{}, 120, {2, 5, 3, -2, -5, -3}] (* Harvey P. Dale, Dec 27 2022 *)
PROG
(PARI) {m=104; a=2; b=5; print1(a=2, ", ", b=5, ", "); for(n=2, m, print1(c=b-a, ", "); a=b; b=c)} /* Klaus Brockhaus, Jul 30 2007 */
(Magma) m:=105; [ [2, 5, 3, -2, -5, -3][ (n-1) mod 6 + 1 ]: n in [1..m] ]; /* Klaus Brockhaus, Jul 30 2007 */
CROSSREFS
Sequence in context: A078375 A362090 A065261 * A222760 A302130 A156637
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Jul 21 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jul 30 2007
STATUS
approved