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A230149
The number of multinomial coefficients over partitions with value equal to 5.
7
0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 3, 3, 2, 3, 4, 4, 4, 3, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 7, 7, 8, 8, 7, 8, 9, 9, 9, 8, 10, 10, 10, 10, 10, 11, 11, 11, 12, 11, 12, 12, 13, 13, 12, 13, 14, 14, 14, 13, 15, 15, 15, 15, 15, 16, 16, 16, 17, 16, 17, 17, 18, 18, 17
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.
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
Sequence in context: A056812 A210721 A082533 * A050373 A306433 A308174
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