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Search: id:A109152
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| A109152 |
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Triangle T, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0, where T^2 is the matrix square of T. |
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+0
6
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| 1, 1, 1, 2, 2, 1, 6, 4, 3, 1, 22, 14, 6, 4, 1, 94, 56, 24, 8, 5, 1, 450, 262, 102, 36, 10, 6, 1, 2366, 1348, 516, 160, 50, 12, 7, 1, 13450, 7574, 2814, 868, 230, 66, 14, 8, 1, 81802, 45616, 16752, 4968, 1330, 312, 84, 16, 9, 1, 527826, 292442, 106026, 31148, 7930
(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^(m+1) = SHIFT_UP(T^m - T^(m-1)) - D*T^(m-1) for all m where diagonal matrix D = [0, 1, 2, 3, ...] and SHIFT_UP shifts each column up 1 row.
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EXAMPLE
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Triangle T begins:
1;
1,1;
2,2,1;
6,4,3,1;
22,14,6,4,1;
94,56,24,8,5,1;
450,262,102,36,10,6,1;
2366,1348,516,160,50,12,7,1; ...
Matrix square T^2 starts:
1;
2,1;
6,4,1;
22,14,6,1;
94,56,24,8,1; ...
which equals SHIFT_UP(T) - D where
D is the diagonal matrix [0,1,2,3,...].
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PROGRAM
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(PARI) {T(n, k)=local(M=matrix(n, n, r, c, if(r>=c, T(r-1, c-1)))); if(n<k|k<0, 0, if(n==k|n==0, 1, if(n==k+1, n, (M^2)[n, k+1])))}
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CROSSREFS
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Cf. A109153 (column 0), A109154 (column 1), A109155 (column 2), A109156 (row sums).
Sequence in context: A127082 A065052 A128308 this_sequence A130469 A106381 A064784
Adjacent sequences: A109149 A109150 A109151 this_sequence A109153 A109154 A109155
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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), Jun 20 2005
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