A165192 a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3).

1, 2, 3, 2, 0, -3, -5, -5, -2, 3, 8, 10, 7, -1, -11, -18, -17, -6, 12, 29, 35, 23, -6, -41, -64, -58, -17, 47, 105, 122, 75, -30, -152, -227, -197, -45, 182, 379, 424, 242, -137, -561, -803, -666, -105, 698, 1364, 1469, 771, -593, -2062, -2833, -2240, -178

Offset

0,2

Links

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (1,0,-1).

Formula

a(n) = (-1)^n*A104771(n).

G.f.: (1+x+x^2)/(1-x+x^3).

Example

a(3) = 2 because 2 = 3 - 1 where the 1, 3 on the right of the equals sign are the first and third terms of the series.

Mathematica

LinearRecurrence[{1, 0, -1}, {1, 2, 3}, 80] (* Harvey P. Dale, Apr 13 2012 *)

Prog

(Python)
series = [1, 2, 3]
for i in range(2, 30):
    series.append(series[i] - series[i - 2])
print(series)

Crossrefs

Cf. A104771

Sequence in context: A303121 A332921 A239579 * A104771 A307688 A056888

Adjacent sequences: A165189 A165190 A165191 * A165193 A165194 A165195

Keyword

easy,sign

Author

Ben Paul Thurston, Sep 06 2009

Extensions

Offset corrected and recurrence simplified by R. J. Mathar, Sep 08 2009

More terms from Harvey P. Dale, Apr 13 2012

Status

approved