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A187038
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Row sums of number triangle A187037.
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4
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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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.
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PROG
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(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
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CROSSREFS
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Cf. A187034, A187036, A187037, A269735.
Sequence in context: A007325 A247920 A269735 * A332260 A056619 A324300
Adjacent sequences: A187035 A187036 A187037 * A187039 A187040 A187041
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KEYWORD
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nonn
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AUTHOR
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Paul Barry, Mar 08 2011
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EXTENSIONS
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More terms from Antti Karttunen, Sep 29 2018
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STATUS
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approved
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