A077228 Triangle of compositions with a total that is no more than n into exactly k parts each no more than k.

1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 4, 10, 5, 1, 1, 4, 17, 15, 6, 1, 1, 4, 23, 35, 21, 7, 1, 1, 4, 26, 66, 56, 28, 8, 1, 1, 4, 27, 106, 126, 84, 36, 9, 1, 1, 4, 27, 150, 247, 210, 120, 45, 10, 1, 1, 4, 27, 190, 432, 462, 330, 165, 55, 11, 1, 1, 4, 27, 221, 687, 918, 792, 495, 220, 66

Offset: 0

Author

Henry Bottomley, Oct 30 2002

Keywords

• nonn
• tabl

Examples

			Rows start: 1; 1,1; 1,3,1; 1,4,4,1; 1,4,10,5,1; 1,4,17,15,6,1; 1,4,23,35,21,7,1; etc. T(6,3)=17 since compositions with 3 parts each no more than 3 and a total no more than 6 are: 1+1+1, 1+1+2, 1+1+3, 1+2+1, 1+2+2, 1+2+3, 1+3+1, 1+3+2, 2+1+1, 2+1+2, 2+1+3, 2+2+1, 2+2+2, 2+3+1, 3+1+1, 3+1+2 and 3+2+1.
		

Links

• Index entries for sequences related to compositions

Crossrefs

Rows eventually start like A000312. Central diagonal is A001700. Right hand side and central diagonal is like right hand side of A007318. Cf. A077227.

Formula

T(n, k) =a(n-1, k)+A077227(n, k). If n>=k^2, T(n, k)=n^n. If k<=n<2k, T(n, k)=C(n, k).