OFFSET
1,9
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=5 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,0,0,0,-1).
FORMULA
a(n) = floor((1/4)*(n-1)) +floor((1/5)*(n-1)) -floor((1/5)*n).
a(n) = a(n-4) + a(n-5) - a(n-9). - Charles R Greathouse IV, Oct 11 2013
G.f.: x^6*(1+x+x^2+2*x^3)/((1+x)*(1-x)^2*(1+x^2)*(1+x+x^2+x^3+x^4)). - Bruno Berselli, Oct 11 2013
EXAMPLE
The number 11 has two partitions such that a(10)=5: 1+1+1+1+7 and 2+2+2+2+3.
MAPLE
seq(floor((n-1)*(1/4))+floor((n-1)*(1/5))-floor((1/5)*n), n=1..50)
MATHEMATICA
CoefficientList[Series[x^5 (1 + x + x^2 + 2 x^3)/((1 + x) (1 - x)^2 (1 + x^2) (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 11 2013 *)
PROG
(PARI) a(n)=(n-1)\4-(n%5==0) \\ Charles R Greathouse IV, Oct 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 11 2013
EXTENSIONS
More terms from Bruno Berselli, Oct 11 2013
G.f. adapted to the offset from Vincenzo Librandi, Oct 11 2013
STATUS
approved