A187038 Row sums of number triangle A187037.

1, 2, 3, 2, 0, 2, 5, 2, 0, 2, 2, 2, 0, 2, 7, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 2, 9, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 2, 6, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 2, 11, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 2, 6, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 2, 8, 2, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2

Offset

0,2

Comments

Apparently, apart from signs, same as A269735 (with a shift). If so, the g.f. for this sequence is obtained from that for A269735 by replacing x by -x. - N. J. A. Sloane, Mar 11 2016

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 30 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));
A187038list(up_to) = { my(m1=matrix(up_to, up_to, n, k, A187034downshifted_and_negated(n-1, k-1)), m2 = matsolve(m1, matid(up_to)), v = vector(up_to)); for(n=1, up_to, v[n] = vecsum(m2[n, ])); (v); };
write_A187036_and_A187038list(up_to) = { my(m1=matrix(up_to, up_to, n, k, A187034downshifted_and_negated(n-1, k-1)), m2 = matsolve(m1, matid(up_to)), v187036 = (m2[, 1]~), v187038 = vector(up_to, j, vecsum(m2[j, ]))); for(n=1, up_to, write("b187036.txt", n-1, " ", v187036[n]); write("b187038.txt", n-1, " ", v187038[n])); }; \\ For computing both at the same time
v187038 = A187038list(1+up_to);
A187038(n) = v187038[1+n]; \\ Antti Karttunen, Sep 29 2018

Crossrefs

Cf. A187034, A187036, A187037, A269735.

Sequence in context: A007325 A247920 A269735 * A332260 A056619 A324300

Adjacent sequences: A187035 A187036 A187037 * A187039 A187040 A187041

Keyword

nonn

Author

Paul Barry, Mar 08 2011

Extensions

More terms from Antti Karttunen, Sep 29 2018

Status

approved