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Search: id:A054120
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| A054120 |
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Triangular array T(n,k): start with T(n,0)=T(n,n)=1 for n >= 0; recursively, draw vertical lines through T(n-1,k-1) if present and T(n-1,k) if present; then T(n,k) is the sum of T(i,j) that lie on or between the lines and not below T(n,k). |
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+0
4
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| 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 9, 18, 9, 1, 1, 12, 39, 39, 12, 1, 1, 15, 69, 114, 69, 15, 1, 1, 18, 108, 261, 261, 108, 18, 1, 1, 21, 156, 507, 750, 507, 156, 21, 1, 1, 24, 213, 879, 1779, 1779, 879, 213, 24, 1, 1, 27, 279, 1404, 3672, 5058
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Conjecture: T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1) + T(n-1,k) (except for T(0,0) = 1 and T(2,1) = 3, and assuming that T(n,k) = 0 for elements outside the triangular array). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Sep 20 2007
Conjecture: T(n,k) = A081577(n,k) - A081577(n-2,k-1). (A081577 is Pascal-(1,2,1) array). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Sep 20 2007
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EXAMPLE
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Rows: {1}, {1,1}, {1,3,1}, {1,6,6,1}, ...
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CROSSREFS
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Row sums: A052945.
Sequence in context: A145904 A035582 A109647 this_sequence A114176 A056241 A001263
Adjacent sequences: A054117 A054118 A054119 this_sequence A054121 A054122 A054123
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KEYWORD
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nonn,tabl,eigen
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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