OFFSET
1,3
COMMENTS
m offset is 1, n offset is 2 so 1st entry is T(1,2).
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(m,n) = 2^n - Product_{i=0,...,m-1} F(floor((n + i)/m + 2)) where F(n) is the n-th Fibonacci number.
EXAMPLE
Table begins:
1, 3, 8, 19, 43, 94, 201, 423, 880, ...
0, 2, 7, 17, 39, 88, 192, 408, 855, ...
0, 0, 4, 14, 37, 83, 181, 387, 824, ...
0, 0, 0, 8, 28, 74, 175, 377, 799, ...
0, 0, 0, 0, 16, 56, 148, 350, 781, ...
0, 0, 0, 0, 0, 32, 112, 296, 700, ...
0, 0, 0, 0, 0, 0, 64, 224, 592, ...
0, 0, 0, 0, 0, 0, 0, 128, 448, ...
0, 0, 0, 0, 0, 0, 0, 0, 256, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
.......................................
T(2,3) 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 T(2,3) = 2.
MATHEMATICA
T[m_, n_] := 2^n - Product[Fibonacci[Floor[(n + i)/m + 2]], {i, 0, m - 1}]; Table[T[i, j + 2], {i, 1, 10}, {j, 0, 10}]; Flatten[Table[T[i - j + 1, j + 2], {i, 0, 20}, {j, 0, i}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Nacin, Mar 09 2012
STATUS
approved