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A162745
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A Fibonacci-Pascal triangle.
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1
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1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1, 1, 21, 105, 173, 105, 21, 1, 1, 28, 196, 476, 476, 196, 28, 1, 1, 36, 336, 1120, 1643, 1120, 336, 36, 1, 1, 45, 540, 2352, 4707, 4707, 2352, 540, 45, 1, 1, 55, 825, 4530, 11775, 16040, 11775, 4530, 825, 55, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = Sum_{j=0..n} C(n,j)*C(n-j,2(k-j))*Fibonacci(k-j+1).
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 3, 1;
1, 6, 6, 1;
1, 10, 20, 10, 1;
1, 15, 50, 50, 15, 1;
1, 21, 105, 173, 105, 21, 1;
1, 28, 196, 476, 476, 196, 28, 1;
1, 36, 336, 1120, 1643, 1120, 336, 36, 1;
1, 45, 540, 2352, 4707, 4707, 2352, 540, 45, 1;
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PROG
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(PARI) T(n, k)=sum(j=0, n, binomial(n, j)*binomial(n-j, 2*(k-j))*fibonacci(k-j+1));
row(n) = vector(n+1, k, T(n, k-1)); \\ Michel Marcus, Nov 11 2022
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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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