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

Author

Paul Barry, Mar 08 2011

Keywords

• nonn

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.

Crossrefs

Cf. A187034, A187036, A187037, A269735.

Programs

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

Extensions

More terms from Antti Karttunen, Sep 29 2018