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A230128
The number of multinomial coefficients over partitions with value equal to 4.
6
0, 0, 0, 0, 1, 1, 2, 1, 2, 3, 3, 2, 4, 4, 4, 4, 5, 5, 6, 5, 6, 7, 7, 6, 8, 8, 8, 8, 9, 9, 10, 9, 10, 11, 11, 10, 12, 12, 12, 12, 13, 13, 14, 13, 14, 15, 15, 14, 16, 16, 16, 16, 17, 17, 18, 17, 18, 19, 19, 18, 20, 20, 20, 20, 21, 21, 22, 21, 22, 23, 23, 22, 24
OFFSET
1,7
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=4 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
FORMULA
a(n) = floor((1/3)*(n-1)) + floor((1/4)*(n-1)) - floor((1/4)*n).
a(n) = a(n-3)+a(n-4)-a(n-7). G.f.: x^5*(2*x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^2+x+1)). - Colin Barker, Mar 06 2014
EXAMPLE
The number 10 has three partitions such that a(10)=4: 1+1+1+7, 1+3+3+3 and 2+2+2+4.
MAPLE
seq(floor((n-1)*(1/3))+floor((n-1)*(1/4))-floor((1/4)*n), n=1..50)
MATHEMATICA
Table[Floor[(1/3) (n-1)] + Floor[(1/4) (n-1)] - Floor[(1/4) n], {n, 1, 100}] (* Vincenzo Librandi, Oct 11 2013 *)
PROG
(Magma) [Floor((1/3)*(n-1))+Floor((1/4)*(n-1))-Floor((1/4)*n): n in [1..100]]; // Vincenzo Librandi, Oct 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 10 2013
EXTENSIONS
More terms from Vincenzo Librandi, Oct 11 2013
STATUS
approved