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A038792 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. 12
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; text; internal format)
OFFSET

1,5

COMMENTS

Antidiagonal sums: A029907.

Main diagonal: A001519 (odd-indexed Fibonacci numbers).

Next diagonal: A001906 (even-indexed Fibonacci numbers).

LINKS

Table of n, a(n) for n=1..73.

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.

C. Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40 (4) (2002) 328-338, Example 4.

FORMULA

G.f.: x*y*(1-x*y)/((x*y+x-1)*(x*y+y-1)). - Mark van Hoeij, Nov 09 2011

EXAMPLE

From Clark Kimberling, Jun 20 2011: (Start)

Northwest corner begins

  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, ...

(End)

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

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}]]

CROSSREFS

Cf. A000045.

Sequence in context: A259874 A256141 A072704 * A196416 A306697 A297845

Adjacent sequences:  A038789 A038790 A038791 * A038793 A038794 A038795

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, May 02 2000

EXTENSIONS

New description from Benoit Cloitre, Aug 05 2003

Updated from pre-2003 triangular format to present rectangular, from Clark Kimberling, Jun 20 2011

STATUS

approved

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Last modified March 25 15:02 EDT 2019. Contains 321470 sequences. (Running on oeis4.)