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A113953
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A Jacobsthal triangle.
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3
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1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, 0, 4, 6, 1, 0, 0, 0, 12, 8, 1, 0, 0, 0, 8, 24, 10, 1, 0, 0, 0, 0, 32, 40, 12, 1, 0, 0, 0, 0, 16, 80, 60, 14, 1, 0, 0, 0, 0, 0, 80, 160, 84, 16, 1, 0, 0, 0, 0, 0, 32, 240, 280, 112, 18, 1, 0, 0, 0, 0, 0, 0, 192, 560, 448, 144, 20, 1, 0, 0, 0, 0, 0, 0, 64, 672, 1120, 672, 180, 22, 1
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OFFSET
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0,5
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COMMENTS
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Rows sums are the Jacobsthal numbers A001045(n+1).
Antidiagonal sums are the Padovan-Jacobsthal numbers A052947.
Inverse is (1,xc(-2x)), c(x) the g.f. of A000108, with general term k*C(2n-k-1,n-k)(-2)^(n - k)/n.
Triangle read by rows given by (0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 01 2013
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LINKS
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FORMULA
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G.f.: 1/(1-xy(1+2x)).
Riordan array (1, x(1+2x)).
T(n,k) = 2^(n-k)*binomial(k, n-k).
T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1), T(0,0) = 1, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Nov 01 2013
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EXAMPLE
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Rows begin
1;
0, 1;
0, 2, 1;
0, 0, 4, 1;
0, 0, 4, 6, 1;
0, 0, 0, 12, 8, 1;
0, 0, 0, 8, 24, 10, 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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