A191687 - OEIS

%I #14 Oct 20 2024 04:06:49

%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 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 Top left corner:

%e   1, 1, 1,  1,  1,...

%e   1, 1, 2,  2,  3,...

%e   1, 2, 5,  8, 13,...

%e   1, 4,14, 32, 63,...

%e   1, 8,41,128,313,...

%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