A191687 Table T(n,k)=[Ceiling[1/2*((k+1)^n+(1+(-1)^k)/2)] read by antidiagonals

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

Top left corner

1, 1, 1, 1, 5,...

1, 1, 2, 2, 3,...

1, 2, 5, 8, 13,...

1, 4,14, 32, 63,...

1, 8,41,128,313,...

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

T(n,k) is the number of compositions of even natural numbers into n parts <=k

Links

Table of n, a(n) for n=1..52.

Adi Dani, Restricted compositions of natural numbers

Example

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}]]

Crossrefs

Rows sums gives: A000012, A004526, A000982, A036486, A171714, A191484, A191489, A191494, A191495, A191496

Columns sums gives: A000012, A000079, A007051, A004171, A034478, A081341, A034494, A092811, A083884, A093143

Sequence in context: A133135 A292189 A284992 * A322190 A177254 A340910

Adjacent sequences: A191684 A191685 A191686 * A191688 A191689 A191690

Keyword

nonn,tabl

Author

Adi Dani, Jun 11 2011

Status

approved