OFFSET
0,6
COMMENTS
The first differences b(n)=a(n+1)-a(n) obey the recurrence b(n+1)-2b(n) = (-3,3,-2,3,-3,2), continued with period 6.
The 2nd differences c(n)=b(n+1)-b(n) obey the recurrence c(n+1)-2c(n) = (6,-5,5,-6,5,-5), periodically continued with period 6.
The hexaperiodic coefficients in these recurrences for A113405, A131666 and their higher order differences define a table,
0, 0, 1, 0, 0, -1 <- A113405
0, 1, -1, 0, -1, 1 <- A131666
1, -2, 1, -1, 2, -1 <- a(n)
-3, 3, -2, 3, -3, 2 <- b(n)
6, -5, 5, -6, 5, -5 <- c(n)
-11,10,-11, 11,-10, 11
21,-21,22,-21, 21,-22
...
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).
FORMULA
a(n+1)-2a(n) = A131556(n), a sequence with period length 6.
G.f.: -(x-1)^2*x / ((x+1)*(2*x-1)*(x^2-x+1)). - Colin Barker, Mar 04 2013
MATHEMATICA
LinearRecurrence[{2, 0, -1, 2}, {0, 1, 0, 1}, 40] (* Harvey P. Dale, Jan 15 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Curtz, Sep 24 2007
EXTENSIONS
Edited by R. J. Mathar, Jun 28 2008
STATUS
approved