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A332056 a(1) = 1, then a(n+1) = a(n) - (-1)^a(n) Sum_{k=1..n} a(k): if a(n) is odd, add the partial sum, else subtract. 4
1, 2, -1, 1, 4, -3, 1, 6, -5, 1, 8, -7, 1, 10, -9, 1, 12, -11, 1, 14, -13, 1, 16, -15, 1, 18, -17, 1, 20, -19, 1, 22, -21, 1, 24, -23, 1, 26, -25, 1, 28, -27, 1, 30, -29, 1, 32, -31, 1, 34, -33, 1, 36, -35, 1, 38, -37, 1, 40, -39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The terms display a 3-quasiperiodic pattern (1, 2m, 1-2m), m = 1, 2, 3, ...

LINKS

Table of n, a(n) for n=1..60.

Eric Angelini, Re: Add or subtract my cumulative sum of terms, SeqFan list, Feb 24 2020.

FORMULA

a(3k-2) = 1, a(3k-1) = 2k, a(3k) = 1 - 2k, for all k >= 1.

Conjectures from Colin Barker, Feb 25 2020: (Start)

G.f.: x*(1 + x)*(1 + 2*x + x^3) / ((1 - x)*(1 + x + x^2)^2).

a(n) = -a(n-1) - a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>5.

(End)

EXAMPLE

a(1) = 1 is odd, so we add the partial sum (so far equal to a(1)) to get the next term, a(2) = 2.

Now a(2) = 2 is even, so we subtract the partial sum 1 + 2 = 3 to get a(3) = -1.

And so on.

PROG

(PARI) s=-a=1; vector(100, n, a-=(-1)^a*s+=a)

(PARI) apply( {A332056(n)=[1-n\3*2, 1, n\/3*2][n%3+1]}, [1..99])

CROSSREFS

See A332057 for the partial sums.

Sequence in context: A264831 A264728 A306790 * A074744 A010360 A262357

Adjacent sequences:  A332053 A332054 A332055 * A332057 A332058 A332059

KEYWORD

sign

AUTHOR

Eric Angelini and M. F. Hasler, Feb 24 2020

STATUS

approved

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Last modified August 10 12:39 EDT 2020. Contains 336379 sequences. (Running on oeis4.)