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

0,5

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to compositions

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).

Example

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.

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.

Sequence in context: A036040 A080575 A205117 * A049687 A362036 A132735

Adjacent sequences: A077225 A077226 A077227 * A077229 A077230 A077231

Keyword

nonn,tabl

Author

Henry Bottomley, Oct 30 2002

Status

approved