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A209436 Table of a(n,m) = number of subsets of {1,...,n} which contain two elements whose difference is m+1. 4
0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 8, 2, 0, 0, 0, 19, 7, 0, 0, 0, 0, 43, 17, 4, 0, 0, 0, 0, 94, 39, 14, 0, 0, 0, 0, 0, 201, 88, 37, 8, 0, 0, 0, 0, 0, 423, 192, 83, 28, 0, 0, 0, 0, 0, 0, 880, 408, 181, 74, 16, 0, 0, 0, 0, 0, 0, 1815, 855, 387, 175, 56, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

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

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

FORMULA

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

EXAMPLE

Table begins:

0,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ...

0,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ...

1,   0,   0,   0,   0,   0,   0,   0,   0,   0, 0, ...

3,   2,   0,   0,   0,   0,   0,   0,   0,   0, 0, ...

8,   7,   4,   0,   0,   0,   0,   0,   0,   0, 0, ...

19,  17,  14,  8,   0,   0,   0,   0,   0,   0, 0, ...

43,  39,  37,  28,  16,  0,   0,   0,   0,   0, 0, ...

94,  88,  83,  74,  56,  32,  0,   0,   0,   0, 0, ...

201, 192, 181, 175, 148, 112, 64,  0,   0,   0, 0, ...

423, 408, 387, 377, 350, 296, 224, 128, 0,   0, 0, ...

880, 855, 824, 799, 781, 700, 592, 448, 256, 0, 0, ...

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

a(3,1) is the number of subsets of {1,2,3} containing two elements whose difference is two.  There are 2 of these: {1,3} and {1,2,3} so a(1,3) = 2.

MATHEMATICA

a[n_, m_] := 2^n - Product[Fibonacci[Floor[(n + i)/(m + 1) + 2]], {i, 0, m}]; Flatten[Table[a[j - i, i], {j, 0, 20}, {i, 0, j}]]

CROSSREFS

Cf. A209434, A209435, A209437.

Sequence in context: A115859 A241663 A129170 * A229121 A190609 A057389

Adjacent sequences:  A209433 A209434 A209435 * A209437 A209438 A209439

KEYWORD

nonn,tabl

AUTHOR

David Nacin, Mar 09 2012

STATUS

approved

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Last modified December 15 11:05 EST 2018. Contains 318148 sequences. (Running on oeis4.)