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%I #10 Apr 18 2013 02:51:51
%S 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,
%T 63,18,4,1,1,64,365,512,313,108,25,4,1,1,128,1094,2048,1563,648,172,
%U 32,5,1
%N Table T(n,k)=[Ceiling[1/2*((k+1)^n+(1+(-1)^k)/2)] read by antidiagonals
%C Top left corner
%C 1, 1, 1, 1, 5,...
%C 1, 1, 2, 2, 3,...
%C 1, 2, 5, 8, 13,...
%C 1, 4,14, 32, 63,...
%C 1, 8,41,128,313,...
%C ......................
%C T(n,k) is the number of compositions of even natural numbers into n parts <=k
%H Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%e T(2,4)=13: there are 13 compositions of even natural numbers into 2 parts <=4
%e 0: (0,0);
%e 2: (0,2), (2,0), (1,1);
%e 4: (0,4), (4,0), (1,3), (3,1), (2,2);
%e 6: (2,4), (4,2), (3,3);
%e 8: (4,4).
%t Table[Table[Ceiling[1/2*((k+1)^n+(1+(-1)^k)/2)],{n,0,9},{k,0,9}]]
%Y Rows sums gives: A000012, A004526, A000982, A036486, A171714, A191484, A191489, A191494, A191495, A191496
%Y Columns sums gives: A000012, A000079, A007051, A004171, A034478, A081341, A034494, A092811, A083884, A093143
%K nonn,tabl
%O 1,5
%A _Adi Dani_, Jun 11 2011
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