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A187036
An eigensequence of A187034.
4
1, 1, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0
COMMENTS
First column of A187037.
Appears to be a signed indicator function for A027383.
The above claim is true at least up to n=1022. For construction, see Barry, 2011. Although the paper doesn't treat especially this sequence, it outlines a general method for creating such sequences. - Antti Karttunen, Sep 29 2018
LINKS
P. Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv:1107.5490 [math.CO], 2011.
PROG
(PARI)
up_to = 128;
A187034aux(n, k) = if(k>n, 0, if(n<=2*k, (-1)^(n-k), 0));
A187034downshifted_and_negated(n, k) = if(k==n, 1, -A187034aux(n-1, k));
A187036list(up_to) = { my(m1=matrix(up_to, up_to, n, k, A187034downshifted_and_negated(n-1, k-1)), m2 = matsolve(m1, matid(up_to))); (m2[, 1]~); };
v187036 = A187036list(1+up_to);
A187036(n) = v187036[1+n]; \\ (or use code in A187038) - Antti Karttunen, Sep 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Barry, Mar 08 2011
EXTENSIONS
More terms from Antti Karttunen, Sep 29 2018
STATUS
approved