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Search: id:A047080
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| A047080 |
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Triangular array T read by rows: T(h,k)=number of paths from (0,0) to (k,h-k) using step-vectors (0,1), (1,0), (1,1) with no right angles between pairs of consecutive steps. |
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+0
9
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| 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 4, 5, 5, 4, 1, 1, 5, 8, 9, 8, 5, 1, 1, 6, 12, 15, 15, 12, 6, 1, 1, 7, 17, 24, 27, 24, 17, 7, 1, 1, 8, 23, 37, 46, 46, 37, 23, 8, 1, 1, 9, 30, 55, 75, 83, 75, 55, 30, 9, 1, 1, 10, 38, 79, 118, 143, 143, 118, 79, 38, 10, 1
(list; table; graph; listen)
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OFFSET
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0,8
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FORMULA
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T(h, k) = T(h-1, k-1) + T(h-1, k) - T(h-4, k-2); Writing T(h, k) = F(h-k, k), generating function for F is (1-xy)/(1-x-y+x^2y^2)
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EXAMPLE
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E.g. row 3 consists of T(3,0)=1; T(3,1)=2; T(3,2)=2; T(3,3)=1.
1; 1,1; 1,1,1; 1,2,2,1; 1,3,3,3,1; ...
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CROSSREFS
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Adjacent sequences: A047077 A047078 A047079 this_sequence A047081 A047082 A047083
Sequence in context: A102481 A110659 A100522 this_sequence A036064 A090706 A050935
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Sequence recomputed to correct terms from 23rd onward. Added recurrence and generating function (Michael L. Catalano-Johnson (mcj(AT)pa.wagner, com), Jan 14 2000).
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