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0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 3, 1, 1, 0, 5, 5, 4, 1, 1, 0, 8, 11, 7, 5, 1, 1, 0, 13, 22, 18, 9, 6, 1, 1, 0, 21, 48, 39, 26, 11, 7, 1, 1, 0, 34, 106, 94, 59, 35, 13, 8, 1, 1, 0, 55, 245, 223, 152, 82, 45, 15, 9, 1, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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LINKS
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FORMULA
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R(n,k) = k*Sum_{i=0..(n-k)} Fibonacci(i)*Sum_{j=k..(n-i)} binomial(2*j-k-1,j-1)*(-1)^(n-j-i)*binomial(n-i,j))/(n-i)), k>1.
R(n,0) = Fibonacci(n).
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EXAMPLE
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Array begins:
0;
1, 0;
1, 1, 0;
2, 1, 1, 0;
3, 3, 1, 1, 0;
5, 5, 4, 1, 1, 0;
8, 11, 7, 5, 1, 1, 0;
13, 22, 18, 9, 6, 1, 1, 0;
21, 48, 39, 26, 11, 7, 1, 1, 0;
34, 106, 94, 59, 35, 13, 8, 1, 1, 0;
55, 245, 223, 152, 82, 45, 15, 9, 1, 1, 0;
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MAPLE
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A185813 := proc(n, k) if n = k then 0; elif k = 0 then combinat[fibonacci](n) ; else k*add(1/(n-i)*combinat[fibonacci](i)*add(binomial(2*j-k-1, j-1) *(-1)^(n-j-i) *binomial(n-i, j), j=k..n-i), i=0..n-k) ; end if; end proc:
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MATHEMATICA
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r[n_, k_] := k*Sum[((-1)^(n+k-i)*Fibonacci[i]*(n-i)!*HypergeometricPFQ[{k/2 + 1/2, k/2, i+k-n}, {k, k+1}, 4])/((n-i)*k!*(n-i-k)!), {i, 0, n-k}]; r[n_, 0] := Fibonacci[n]; Table[r[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 21 2013 *)
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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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