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A191687
Table T(n,k) = ceiling((1/2)*((k+1)^n+(1+(-1)^k)/2)) read by antidiagonals.
0
1, 1, 1, 1, 2, 2, 1, 1, 4, 5, 2, 1, 1, 8, 14, 8, 3, 1, 1, 16, 41, 32, 13, 3, 1, 1, 32, 122, 128, 63, 18, 4, 1, 1, 64, 365, 512, 313, 108, 25, 4, 1, 1, 128, 1094, 2048, 1563, 648, 172, 32, 5, 1
OFFSET
1,5
COMMENTS
T(n,k) is the number of compositions of even natural numbers into n parts <= k.
EXAMPLE
Top left corner:
1, 1, 1, 1, 1,...
1, 1, 2, 2, 3,...
1, 2, 5, 8, 13,...
1, 4,14, 32, 63,...
1, 8,41,128,313,...
T(2,4)=13: there are 13 compositions of even natural numbers into 2 parts <=4
0: (0,0);
2: (0,2), (2,0), (1,1);
4: (0,4), (4,0), (1,3), (3,1), (2,2);
6: (2,4), (4,2), (3,3);
8: (4,4).
MATHEMATICA
Table[Table[Ceiling[1/2*((k+1)^n+(1+(-1)^k)/2)], {n, 0, 9}, {k, 0, 9}]]
KEYWORD
nonn,tabl
AUTHOR
Adi Dani, Jun 11 2011
STATUS
approved