A195084 -id:A195084 - cp's OEIS frontend

A227805 Sum of even numbers starting at 2, alternating signs.

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

D.Wilde, Aug 02 2013

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

			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.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

Cf. A195084.

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 *)

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

cp's OEIS Frontend

A227805 Sum of even numbers starting at 2, alternating signs.

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