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Search: id:A141751
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| A141751 |
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Triangle, read by rows, where T(n,k) = [T(n-1,k-1)*T(n-1,k) + 1]/T(n-2,k-1) for 0<k<n with T(n,n) = 1 for n>=0 and T(n,0) = Fibonacci(2*n-1) for n>=1. |
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+0
2
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| 1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 13, 13, 8, 4, 1, 34, 34, 21, 11, 5, 1, 89, 89, 55, 29, 14, 6, 1, 233, 233, 144, 76, 37, 17, 7, 1, 610, 610, 377, 199, 97, 45, 20, 8, 1, 1597, 1597, 987, 521, 254, 118, 53, 23, 9, 1, 4181, 4181, 2584, 1364, 665, 309, 139, 61, 26, 10, 1
(list; table; graph; listen)
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OFFSET
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0,4
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FORMULA
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T(n,k) = Fibonacci(2*(n-k)-1) + k*Fibonacci(2*(n-k)) for 0<=k<=n.
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EXAMPLE
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Generating rule.
Given non-zero elements W, X, Y, Z, relatively arranged like so:
.. W .....
.. X Y ...
.... Z ...
then Z = (X*Y + 1)/W.
Triangle begins:
1;
1, 1;
2, 2, 1;
5, 5, 3, 1;
13, 13, 8, 4, 1;
34, 34, 21, 11, 5, 1;
89, 89, 55, 29, 14, 6, 1;
233, 233, 144, 76, 37, 17, 7, 1;
610, 610, 377, 199, 97, 45, 20, 8, 1;
1597, 1597, 987, 521, 254, 118, 53, 23, 9, 1;
4181, 4181, 2584, 1364, 665, 309, 139, 61, 26, 10, 1; ...
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PROGRAM
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(PARI) {T(n, k)=if(n<k|k<0, 0, if(n==k, 1, if(k==0, fibonacci(2*n-1), (T(n-1, k-1)*T(n-1, k)+1)/T(n-2, k-1))))}
(PARI) {T(n, k)=fibonacci(2*(n-k))*k+fibonacci(2*(n-k)-1)}
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CROSSREFS
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Cf. row sums: A141752; columns: A001519, A001906, A002878, A054486, A054492, A055267, A055273, A055849.
Sequence in context: A079220 A123971 A114292 this_sequence A079222 A033184 A110488
Adjacent sequences: A141748 A141749 A141750 this_sequence A141752 A141753 A141754
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 04 2008
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