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A285935
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Square array a(n, m) read by antidiagonals whose g.f. is 1 / ((1-x)^2 * (1-y)^2 - x*y).
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0
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1, 2, 2, 3, 5, 3, 4, 10, 10, 4, 5, 18, 26, 18, 5, 6, 30, 58, 58, 30, 6, 7, 47, 116, 153, 116, 47, 7, 8, 70, 214, 354, 354, 214, 70, 8, 9, 100, 371, 746, 931, 746, 371, 100, 9, 10, 138, 612, 1464, 2204, 2204, 1464, 612, 138, 10, 11, 185, 969, 2714, 4816, 5794
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f. Sum_{n>=0, m>=0} a(n, m) * x^n * y^m = 1 / ((1-x)^2 * (1-y)^2 - x*y).
T(n, k) := a(n-k, k) where 0 <= k <= n.
a(n, m) = a(m, n) = T(n+m, n), T(n, 0) = a(n, 0) = n+1, if n>=0, m>=0.
Row sums are (-1)^(n+1) * A113067(n+1).
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EXAMPLE
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a(n,m) 0 1 2 3
----+--- --- --- ---
0 | 1 2 3 4
1 | 2 5 10 18
2 | 3 10 26 58
3 | 4 18 58 153
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MATHEMATICA
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a[n_, m_] := SeriesCoefficient[1/((1-x)^2*(1-y)^2-x*y), {x, 0, n}, {y, 0, m}];
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PROG
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(PARI) {a(n, m) = if( n<0 || m<0, 0, polcoeff( polcoeff( -1/(x*y-sqr(1-x-y+x*y))*(1+x*O(x^n))*(1+y*O(y^k)), n), m))};
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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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