OFFSET
0,4
COMMENTS
The 3-wave sequence with initial values a, b, c is formed by the following construction:
a.......a+b+c............3a+5b+6c...
..b...b+c...a+2b+2c..2a+4b+5c...
....c..........a+2b+3c...
REFERENCES
J. Kappraff, Beyond Measure, World Scientific, Inc. 2002, p. 497.
LINKS
F. v. Lamoen, Wave sequences
Index entries for linear recurrences with constant coefficients, signature (0, 2, 0, 1, 0, -1).
FORMULA
a(n) = a(n-1) + a(n-2) if n is odd,
a(n) = a(n-1) + a(n-4) if n is even.
Also: a(n) = 2*a(n-2) + a(n-4) - a(n-6).
G.f.: (1 + x - x^2)/(1 - 2*x^2 - x^4 + x^6).
PROG
(PARI) a(n)=if(n>-1, polcoeff((1+x-x^2)/(1-2*x^2-x^4+x^6)+x*O(x^n), n), if(n<-3, polcoeff((1-x-x^2)/(1-x^2-2*x^4+x^6)+O(x^(-3-n)), -4-n), 0))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Edited by Floor van Lamoen, Feb 05 2002
STATUS
approved