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A209434 Table T(n,m), read by antidiagonals, is the number of subsets of {1,...,n} which do not contain two elements whose difference is m+1. 4
1, 2, 1, 3, 2, 1, 5, 4, 2, 1, 8, 6, 4, 2, 1, 13, 9, 8, 4, 2, 1, 21, 15, 12, 8, 4, 2, 1, 34, 25, 18, 16, 8, 4, 2, 1, 55, 40, 27, 24, 16, 8, 4, 2, 1, 89, 64, 45, 36, 32, 16, 8, 4, 2, 1, 144, 104, 75, 54, 48, 32, 16, 8, 4, 2, 1, 233, 169, 125, 81, 72, 64, 32 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

1st column is the Fibonacci sequence.

REFERENCES

M. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461 doi:10.1016/j.amc.2009.12.069, Table 1.

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 antidiagonals, flattened

M. Tetiva, Subsets that make no difference d, Mathematics Magazine 84 (2011), no. 4, 300-301.

FORMULA

T(n,m) = Product_{i=0 to m} F(floor[(n + i)/(m + 1) + 2]) where F(n) is the n-th Fibonacci number.

EXAMPLE

Table begins:

1,   1,   1,   1,   1,   1,   1,   1,   1,   1,    1,    ...

2,   2,   2,   2,   2,   2,   2,   2,   2,   2,    2,    ...

3,   4,   4,   4,   4,   4,   4,   4,   4,   4,    4,    ...

5,   6,   8,   8,   8,   8,   8,   8,   8,   8,    8,    ...

8,   9,   12,  16,  16,  16,  16,  16,  16,  16,   16,   ...

13,  15,  18,  24,  32,  32,  32,  32,  32,  32,   32,   ...

21,  25,  27,  36,  48,  64,  64,  64,  64,  64,   64,   ...

34,  40,  45,  54,  72,  96,  128, 128, 128, 128,  128,  ...

55,  64,  75,  81,  108, 144, 192, 256, 256, 256,  256,  ...

89,  104, 125, 135, 162, 216, 288, 384, 512, 512,  512,  ...

144, 169, 200, 225, 243, 324, 432, 576, 768, 1024, 1024, ...

............................................................

MATHEMATICA

a[n_, m_] := Product[Fibonacci[Floor[(n + i)/(m + 1) + 2]], {i, 0, m}]; Flatten[Table[a[j - i, i], {j, 0, 30}, {i, 0, j}]]

CROSSREFS

Cf. A209435, A209436, A209437. Columns: A006498, A006500, A031923, A208742, A208743, A009641

Sequence in context: A119441 A322083 A058399 * A207611 A320973 A058400

Adjacent sequences:  A209431 A209432 A209433 * A209435 A209436 A209437

KEYWORD

nonn,tabl

AUTHOR

David Nacin, Mar 09 2012

STATUS

approved

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Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)