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A126030
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Riordan array (1/(1+x^3),x/(1+x^3)).
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1
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1, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, -3, 0, 0, 1, 1, 0, 0, -4, 0, 0, 1, 0, 3, 0, 0, -5, 0, 0, 1, 0, 0, 6, 0, 0, -6, 0, 0, 1, -1, 0, 0, 10, 0, 0, -7, 0, 0, 1, 0, -4, 0, 0, 15, 0, 0
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OFFSET
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0,12
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COMMENTS
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Inverse is A111373. Row sums are A050935(n+2). Diagonal sums are an alternating sign version of A000931(n+3) with g.f. 1/(1-x^2+x^3).
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LINKS
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FORMULA
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Number triangle T(n,k)=C(k+(n-k)/3,(n-k)/3)*(-1)^(n-k)*(2*cos(2*pi*(n-k)/3)+1)/3
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EXAMPLE
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Triangle begins
.1,
.0, 1,
.0, 0, 1,
.-1, 0, 0, 1,
.0, -2, 0, 0, 1,
.0, 0, -3, 0, 0, 1,
.1, 0, 0, -4, 0, 0, 1,
.0, 3, 0, 0, -5, 0, 0, 1,
.0, 0, 6, 0, 0, -6, 0, 0, 1,
.-1, 0, 0, 10, 0, 0, -7, 0, 0, 1,
.0, -4, 0, 0, 15, 0, 0, -8, 0, 0, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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