OFFSET
1,5
COMMENTS
a(n) is also the number of weak compositions of n into n parts in which at least four parts are zero.
FORMULA
a(n) = binomial(2*n-1,n) - binomial(n,2)*binomial(n-1,2) - binomial(n,3)*binomial(n-1,3) - n*(n-1) - 1.
EXAMPLE
a(6)=81 since 6 can be written as 6+0+0+0+0+0, 0+6+0+0+0+0, etc. (6 such compositions); 5+1+0+0+0+0 (30 such compositions); 4+2+0+0+0+0 (30 such compositions); 3+3+0+0+0+0 (15 such compositions).
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Mar 09 2024
STATUS
approved