login
A227805
Sum of even numbers starting at 2, alternating signs.
1
2, 6, 0, 8, -2, 10, -4, 12, -6, 14, -8, 16, -10, 18, -12, 20, -14, 22, -16, 24, -18, 26, -20, 28, -22, 30, -24, 32, -26, 34, -28, 36, -30, 38, -32, 40, -34, 42, -36, 44, -38, 46, -40, 48, -42, 50, -44, 52, -46, 54, -48, 56, -50, 58, -52, 60, -54, 62, -56, 64
OFFSET
1,1
COMMENTS
Twice A195084. - Joerg Arndt, Aug 14 2013
The 1st, 3rd, 5th, 7th, ... "terms" increase by 2, the 2nd, 4th, 6th, 8th, ... decrease by 2. Also the difference between the terms goes up by 2 each time. For example, the difference between 6 and 0 = 6, difference between 0 and 8 = 8, difference between 8 and -2 = 10, and so on.
Also the sequence seems to "mirror" a few terms before the 6, i.e.: -4, 10, -2, 8, 0, 6, 2, 4,[mirror],4, 2, 6, 0, 8, -2
FORMULA
a(n) = 2 * A195084(n). - Joerg Arndt, Aug 14 2013
G.f.: 2*x*(1+4*x+2*x^2)/((1-x)*(1+x)^2). - Joerg Arndt, Aug 14 2013
EXAMPLE
Using the sequence 2+4-6+8-10+12-14-16 gives (2+4)=6, (6-6)=0, (0+8)=8, (8-10)=-2, (-2+12)=10, etc., giving the sequence 6,0,8,-2,10,-4,12,-6,14,-8.
MATHEMATICA
nn = 100; s = 2 Range[2, nn]*Table[(-1)^i, {i, 2, nn}]; s = Join[{2}, s]; Accumulate[s] (* T. D. Noe, Aug 13 2013 *)
CROSSREFS
Cf. A195084.
Sequence in context: A229586 A294789 A197035 * A267314 A180314 A065344
KEYWORD
sign,less
AUTHOR
D.Wilde, Aug 02 2013
STATUS
approved