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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 (list; graph; refs; listen; history; text; internal format)
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 ie: -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 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

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

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Last modified January 25 01:44 EST 2020. Contains 331229 sequences. (Running on oeis4.)