A187036 An eigensequence of A187034.

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

Antti Karttunen, Table of n, a(n) for n = 0..1025

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

Cf. A027383, A187034, A187037, A187038.

Sequence in context: A323095 A336868 A083187 * A192490 A267133 A080339

Adjacent sequences: A187033 A187034 A187035 * A187037 A187038 A187039

Keyword

sign

Author

Paul Barry, Mar 08 2011

Extensions

More terms from Antti Karttunen, Sep 29 2018

Status

approved