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A038792
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Rectangular array defined by T(i,1)=T(1,j)=1 for i>=0 and j>=0; T(i,j)=Max(T(i-1,j)+T(i-1,j-1); T(i-1,j-1)+T(i,j-1)) for i>=1, j>=1, read by antidiagonals.
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12
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 5, 8, 8, 5, 1, 1, 6, 12, 13, 12, 6, 1, 1, 7, 17, 21, 21, 17, 7, 1, 1, 8, 23, 33, 34, 33, 23, 8, 1, 1, 9, 30, 50, 55, 55, 50, 30, 9, 1, 1, 10, 38, 73, 88, 89, 88, 73, 38, 10, 1, 1, 11, 47, 103, 138, 144, 144
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Antidiagonal sums: A029907.
Main diagonal: A001519 (odd-indexed Fibonacci numbers).
Next diagonal: A001906 (even-indexed Fibonacci numbers).
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LINKS
| A. Dil and I. Mezo, A symmetric algorithm for hyperharmonic and Fibonacci numbers, Appl. Math. Comp. 206 (2008) 942-951. Eq (11), incomplete Fibonacci numbers. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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FORMULA
| G.f. x*y*(1-x*y)/((x*y+x-1)*(x*y+y-1)). - Mark van Hoeij, Nov 09 2011
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EXAMPLE
| Northwest corner:
1....1....1....1....1....1....1....1
1....2....3....4....5....6....7....8
1....3....5....8....12...17...23...30
1....4....8....13...21...33...50...73
1....5....12...21...34...55...88...138
1....6....17...33...55...89...144..232
1....7....23...50...88...144..233..377
[From Clark Kimberling, Jun 20 2011]
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MAPLE
| G := x*y*(1-x*y)/((x*y+x-1)*(x*y+y-1)); G := convert(series(G, x=0, 11), polynom):
for i from 1 to 10 do series(coeff(G, x, i), y=0, 11) od; - Mark van Hoeij, Nov 09 2011
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MATHEMATICA
| f[i_, 0] := 1; f[0, i_] := 1
f[i_, j_] := Max[f[i - 1, j] + f[i - 1, j - 1], f[i - 1, j - 1] + f[i, j - 1]] /; i >= 1 && j >= 1
TableForm[Table[f[i, j], {i, 0, 7}, {j, 0, 7}]]
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CROSSREFS
| Cf. A000045.
Sequence in context: A114225 A193515 A072704 * A196416 A183456 A183342
Adjacent sequences: A038789 A038790 A038791 * A038793 A038794 A038795
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), May 02 2000
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EXTENSIONS
| New description from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2003
Updated from pre-2003 triangular format to present rectangular, from Clark Kimberling, Jun 20 2011
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