

A077228


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


2



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
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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(n1, 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 A132735 A028262
Adjacent sequences: A077225 A077226 A077227 * A077229 A077230 A077231


KEYWORD

nonn,tabl


AUTHOR

Henry Bottomley, Oct 30 2002


STATUS

approved



