Correlations of the first 1124 sequence

Here is some data on the partial sums PS_k(m):=\sum_{i=1}^mx_ix_{i+k} (with the convention x_{i+k}=0 when i+k>m) for small values of k.

Here is a plot for k=1,...12 (click to enlarge)

The final values at m=1124 have some noticeable structure:

firstly, all values of k which are a multiple of 3 are positive while the rest are negative (at least for k\leq 39).

then there are some exact results (accidental ones maybe?), denoting PS_k(1124) by its index k we have: 5=11=35, 29=31, 15=39, 6=-8, 20=-12.

k;PS_k(1124)

1;-259

2;-268

3;239

4;-256

5;-107

6;178

7;-95

8;-178

9;363

10;-160

11;-107

12;210

13;-111

14;-100

15;219

16;-164

17;-181

18;438

19;-193

20;-210

21;303

22;-126

23;-149

24;254

25;-155

26;-184

27;453

28;-164

29;-139

30;236

31;-139

32;-122

33;217

34;-166

35;-107

36;418

37;-195

38;-120

39;219

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