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

1,1

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

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

Adjacent sequences: A227802 A227803 A227804 * A227806 A227807 A227808

Keyword

sign,less

Author

D.Wilde, Aug 02 2013

Status

approved