A359368 Sequence begins 1, 1, 1; for even n > 3, a(n) = a(n/2 - 1) + a(n/2 + 1); for odd n > 3, a(n) = -a((n-1)/2).

1, 1, 1, 2, -1, 3, -1, 0, -2, 5, 1, -2, -3, 3, 1, -3, 0, 5, 2, -1, -5, 3, -1, -2, 2, 1, 3, -2, -3, 0, -1, 1, 3, 2, 0, 2, -5, 4, -2, -3, 1, 2, 5, -6, -3, 1, 1, 1, 2, -1, -2, 5, -1, -1, -3, 0, 2, -2, 3, -4, 0, 1, 1, 2, -1, 3, -3, 3, -2, 4, 0, -5, -2, 6, 5, -7, -4, 1, 2, -1

Offset

1,4

Links

Kevin Ryde, Table of n, a(n) for n = 1..10000

Kevin Ryde, PARI/GP Code

Example

The recurrence for the terms begins:
  a(4) =  a(1) + a(3) =  2
  a(5) = -a(2)        = -1
  a(6) =  a(2) + a(4) =  3
  a(7) = -a(3)        = -1
  a(8) =  a(3) + a(5) =  0
  a(9) = -a(4)        = -2

Mathematica

a[1]=a[2]=a[3]=1; a[n_]:=If[EvenQ[n], a[n/2-1]+a[n/2+1], -a[(n-1)/2]]; Array[a, 80] (* Stefano Spezia, Dec 29 2022 *)

Prog

(Python)
def Seq(n): # generates n terms
    seq = [1, 1, 1]
    k = 0
    while len(seq) < n:
        seq += [seq[k] + seq[k+2]]
        seq += [-1*seq[k+1]]
        k += 1
    return seq
(PARI) \\ See links.

Crossrefs

Sequence in context: A160550 A172038 A331363 * A353490 A377051 A226131

Adjacent sequences: A359365 A359366 A359367 * A359369 A359370 A359371

Keyword

sign,easy

Author

Eden Lippmann, Dec 28 2022

Status

approved