OFFSET
1,6
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=6 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,0,0,0,1).
FORMULA
a(n) = floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)).
G.f.: x^6*(2*x^9-2*x^6-3*x^5-5*x^4-4*x^3-4*x^2-2*x-2) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Oct 15 2013
EXAMPLE
The number 8 has four partitions such that a(8)=6: 1+1+1+1+1+3, 1+1+3+3, 1+2+5 and 1+3+4.
MAPLE
seq(floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)), n=1..50)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 11 2013
EXTENSIONS
More terms from Colin Barker, Mar 06 2014
STATUS
approved