OFFSET
1,17
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=9 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 (0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n).
G.f.: x^10*(2*x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^2+x+1)*(x^4+1)*(x^6+x^3+1)). - Colin Barker, Mar 06 2014
EXAMPLE
The number 25 has three partitions such that a(25)=8: 1+1+1+1+1+1+1+1+17, 1+3+3+3+3+3+3+3+3 and 2+2+2+2+2+2+2+2+9.
MAPLE
seq(floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n)), n=1..99)
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2}, 100] (* Harvey P. Dale, Mar 20 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 14 2013
EXTENSIONS
Typos in formula and Maple code fixed by Colin Barker, Mar 06 2014
STATUS
approved