

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)/((1x)*(1+x)^2). [Joerg Arndt, Aug 14 2013]


EXAMPLE

Using sequence 2+46+810+121416, gives (2+4)=6 (66)=0 (0+8)=8 (810)=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



