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A230258 The number of multinomial coefficients over partitions with value equal to 10. 5
0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 3, 2, 3, 3, 2, 3, 4, 3, 5, 3, 5, 5, 6, 5, 5, 6, 6, 7, 8, 5, 8, 8, 8, 8, 8, 8, 10, 10, 10, 8, 11, 10, 11, 11, 10, 12, 13, 12, 13, 11, 13, 13, 14, 13, 14, 15, 15, 15, 16, 13, 16, 16, 16, 17, 17, 17, 18, 18, 18, 16, 19, 18, 20, 20, 19, 20, 21, 20, 21, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
COMMENTS
The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=10 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 (0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = floor((n-1)*(1/9))+floor((n-1)*(1/10))-floor((1/10)*n)+floor((n-1)*(1/5))+floor((n-1)*(1/6))-floor((1/6)*n)+floor((n+1)*(1/6))-floor((1/5)*n).
G.f.: x^7*(4*x^12 +x^11 +2*x^10 +2*x^9 +2*x^8 +3*x^7 +3*x^6 +2*x^5 +3*x^4 +x^2 +x +1) / ((x -1)^2*(x +1)*(x^2 +x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)*(x^6 +x^3 +1)). - Colin Barker, Mar 06 2014
EXAMPLE
The number 11 has three partitions such that a(11)=10: 1+1+1+1+1+1+1+1+1+2, 1+1+3+3+3 and 1+1+1+4+4.
MAPLE
seq(floor((n-1)*(1/9))+floor((n-1)*(1/10))-floor((1/10)*n)+floor((n-1)*(1/5))+floor((n-1)*(1/6))-floor((1/6)*n)+floor((n+1)*(1/6))-floor((1/5)*n), n=1..80)
CROSSREFS
Sequence in context: A308656 A178775 A124874 * A016459 A242309 A275663
KEYWORD
nonn,easy
AUTHOR
Mircea Merca, Oct 14 2013
STATUS
approved

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Last modified May 18 23:43 EDT 2024. Contains 372666 sequences. (Running on oeis4.)