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User: D.Wilde

D.Wilde has authored 2 sequences.

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

A227832 Sum of odd numbers starting with 1, alternating signs (beginning with plus).

Original entry on oeis.org

1, 4, -1, 6, -3, 8, -5, 10, -7, 12, -9, 14, -11, 16, -13, 18, -15, 20, -17, 22, -19, 24, -21, 26, -23, 28, -25, 30, -27, 32, -29, 34, -31, 36, -33, 38, -35, 40, -37, 42, -39, 44, -41, 46, -43, 48, -45, 50, -47, 52, -49

Offset: 1

D.Wilde, Aug 02 2013

1st,3rd,5th (odd terms) increase by 2, 2nd,4th,6th,8th (even terms) decrease by 2 each time.

			(1+3)=4 (4-5)=-1 (-1+7)=6 (6-9)=-3 (-3+11)=8 (8-13)=-5 (-5+15)=10.

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

Cf. A065164 (absolute values).

a(n) = n*(-1)^n + 2; \\ Michel Marcus, Feb 08 2016

a(n) = -a(n-1) + a(n-2) + a(n-3). - Charles R Greathouse IV, Aug 02 2013

G.f.: x*(2*x^2 + 5*x + 1)/((1-x)*(1+x)^2). a(n) = n*(-1)^n + 2 = A038608(n) + 2. - Ralf Stephan, Aug 07 2013

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User: D.Wilde

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

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