OFFSET
0,2
COMMENTS
0, -1, 0, 2, 3, 6, 12, 15, 20, 30,...
-1, 1, 2, 1, 3, 6, 3, 5, 10, 5,... = a(n-1)
2, 1, -1, 2, 3, -3, 2, 5, -5, 2,...
-1, -2, 3, 1, -6, 5, 3, -10, 7, 5,...
-1, 5, -2, -7, 11, -2, -13, 17, -2, -19,...
6, -7, -5, 18, -13, -11, 30, -19, -17, 42,...
-13, 2, 23, -31, 2, 41, -49, 2, 59, 67,...
15, 21, -54, 33, 39, -90, 51, 57, -126, 69,... multiples of 3
6, -75, 87, 6, -129, 141, 6, -183, 195, 6,... multiples of 3
-81, 162, -81, -135, 270, -135, -189, 378, -189, -243,... multiples of 27
The last line is -27*a(n+3)*A131561(n+1).
The recurrences in the Formula field hold for the array.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
FORMULA
a(n) = 3*a(n-3) -3*a(n-6) +a(n-9) = a(n-1) +2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7). [Ralf Stephan]
From Bruno Berselli, May 29 2013: (Start)
G.f.: (1+x)^3*(1-x+x^2)/((1-x)^2*(1+x+x^2)^2).
a(n) = 2*a(n-3)-a(n-6).
a(3n)*a(3n-1)-a(3n-2) = A016754(n-1), n>0. (End)
EXAMPLE
MATHEMATICA
repeat=20; Table[{1, 2, 1}, {repeat}]*(2*Range[repeat]-1) // Flatten
(* or *) Table[Floor[(2*n+1)/3]*Floor[(2*n+5)/3], {n, -1, 59}] // Differences (* Jean-François Alcover, May 29 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, May 27 2013
STATUS
approved