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A062135
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Odd-numbered columns of Losanitsch triangle A034851 formatted as triangle with an additional first column.
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1
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 6, 3, 1, 0, 3, 10, 12, 4, 1, 0, 3, 19, 28, 20, 5, 1, 0, 4, 28, 66, 60, 30, 6, 1, 0, 4, 44, 126, 170, 110, 42, 7, 1, 0, 5, 60, 236, 396, 365, 182, 56, 8, 1, 0, 5, 85, 396, 868, 1001, 693, 280
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OFFSET
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0,8
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COMMENTS
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Because the sequence of column m=2*k, k >= 1, of A034851 is the partial sum sequence of the one of column m=2*k-1 the present triangle is essentially Losanitsch's triangle A034851.
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LINKS
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FORMULA
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a(n, m)=0 if n<m; a(0, 0)=1, a(n, 0)=0 if n >= 1; a(n, m)= a(n-1, m)+sum(a(k, m-1), k=m-1..n-1) if n+m even and a(n, m)= a(n-1, m)+sum(a(k, m-1), k=m-1..n-1)-binomial((n+m-3)/2, m-1) if n+m odd, n >= m >= 1.
G.f. for column m: x^m*Pe(m, x^2)/(((1-x)^(2*m))*(1+x)^m), m >= 0, with Pe(m, x^2)= sum(A034839(m, k)*x^(2*k), k=0..floor(n/2)), the row polynomial of array A034839 (even-indexed entries of the rows of Pascal's triangle).
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EXAMPLE
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{1}; {0,1}; {0,1,1}; {0,2,2,1}; ...; Pe(4,x^2)=1+6*x^2+x^4.
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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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