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Search: id:A061177
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| A061177 |
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Coefficients of polynomials ((1-x+sqrt(x))^(n+1) - (1-x-sqrt(x))^(n+1))/(2*sqrt(x)). |
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+0
7
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| 1, 2, -2, 3, -5, 3, 4, -8, 8, -4, 5, -10, 11, -10, 5, 6, -10, 6, -6, 10, -6, 7, -7, -14, 29, -14, -7, 7, 8, 0, -56, 120, -120, 56, 0, -8, 9, 12, -126, 288, -365, 288, -126, 12, 9, 10, 30, -228, 540, -770, 770, -540, 228, -30, -10, 11, 55, -363, 858
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The row polynomial pFo(m,x) := sum(a(m,k)*x^k,k=0..m) is the numerator of the g.f. for the m-th column sequence of A060921, the odd part of the bisected Fibonacci triangle.
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FORMULA
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a(n, m)= coefficient of x^m of ((1-x+sqrt(x))^(n+1) - (1-x-sqrt(x))^(n+1))/(2*sqrt(x)).
a(n, m)= sum(((-1)^(m-j))*binomial(n+1, 2*j+1)*binomial(n-2*j, m-j), j=0..m), if 0<= m <= floor(n/2); a(n, m) := ((-1)^n)*a(n, n-m) if floor(n/2) < m <= n; else 0.
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EXAMPLE
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{1}; {2,-2}; {3,-5,3}; {4,-8,8,-4}; ...; pFo(2,x)=3-5*x+3*x^2.
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CROSSREFS
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A060921, A061176 (companion triangle).
Sequence in context: A072039 A131901 A132071 this_sequence A129312 A115262 A128141
Adjacent sequences: A061174 A061175 A061176 this_sequence A061178 A061179 A061180
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KEYWORD
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sign,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
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