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Search: id:A055215
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| A055215 |
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A path-counting array, read by rows: T(i,j)=number of paths from (0,0) to (i-j,j) using steps (1 unit right and 1 unit up) or (1 unit right and 2 units up). |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 2, 3, 4, 2, 1, 1, 1, 2, 3, 5, 4, 2, 1, 1, 1, 2, 3, 5, 7, 4, 2, 1, 1, 1, 2, 3, 5, 8, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 12, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 13, 15, 8, 4, 2, 1, 1, 1, 2, 3, 5, 8, 13, 20, 16
(list; table; graph; listen)
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OFFSET
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1,9
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COMMENT
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If m >= 1 and n >= 2, then T(m+n-1,m) is the number of strings (s(1),s(2),...,s(n)) of nonnegative integers satisfying s(n)=m and 1<=s(k)-s(k-1)<=2 for k=2,3,...,n.
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FORMULA
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T(i, 0)=T(i, i)=1 for i >= 0; T(i, 1)=1 for i >= 1; T(i, j)=T(i-2, j-1)+T(i-3, j-2) for 2<=j<=i-1, i >= 3.
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EXAMPLE
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7=T(8,5) counts these strings: 0135, 0235, 0245, 1235, 1245, 1345, 2345.
Rows: {1}; {1,1}; {1,1,1}; {1,1,2,1}; {1,1,2,2,1}; ...
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CROSSREFS
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T(2n, n)=A000045(n+1), the Fibonacci numbers.
Sequence in context: A037827 A086074 A089723 this_sequence A058398 A091499 A137350
Adjacent sequences: A055212 A055213 A055214 this_sequence A055216 A055217 A055218
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), May 07 2000
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