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A105438
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Triangle, row sums = (Fibonacci numbers - 2).
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4
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1, 2, 1, 3, 2, 1, 4, 4, 2, 1, 5, 6, 5, 2, 1, 6, 9, 8, 6, 2, 1, 7, 12, 14, 10, 7, 2, 1, 8, 16, 20, 20, 12, 8, 2, 1, 9, 20, 30, 30, 27, 14, 9, 2, 1, 10, 25, 40, 50, 42, 35, 16, 10, 2, 1, 11, 30, 55, 70, 77, 56, 44, 18, 11, 2, 1
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OFFSET
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0,2
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COMMENTS
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Row sums = 1, 3, 6, 11, 19, 32, 53...(Fibonacci numbers - 2; starting with F(4)) The first few rows of the triangle are:
Row sums = (Fibonacci numbers - 2; starting 1, 3, 6...).
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LINKS
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FORMULA
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By columns (k = 0, 1, 2...); use partial sum operator on (bin(n, k) numbers repeated).
T(n,k) = Sum_{j=0..n-k} C((j+2k)/2, k)*(1+(-1)^j)+C((j-1+2k)/2, k)*(1-(-1)^j)/2; Riordan array (1/(1-x)^2, x/(1-x^2)). - Paul Barry, Apr 11 2005
T(n,k) = T(n-1,k)+T(n-1,k-1)+T(n-2,k)-T(n-2,k-1)-T(n-3,k), T(0,0)=1, T(1,0)=2, T(1,1)= 1, T(n,k)= 0 if k<0 or if k>n. - Philippe Deléham, Jan 16 2014
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EXAMPLE
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Column 2: 1, 2, 5, 8, 14, 20, 30...is generated by using the partial sum operator on 1, 1, 3, 3, 6, 6, 10, 10...
The first few rows of the triangle are:
1;
2, 1;
3, 2, 1;
4, 4, 2, 1;
5, 6, 5, 2, 1;
6, 9, 8, 6, 2, 1;
7, 12, 14, 10, 7, 2, 1;
8, 16, 20, 20, 12, 8, 2, 1;
9, 20, 30, 30, 27, 14, 9, 2, 1;
10, 25, 40, 50, 42, 35, 16, 10, 2, 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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