A230258 The number of multinomial coefficients over partitions with value equal to 10.

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

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

Table of n, a(n) for n=1..80.

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

Cf. A230128, A230149, A230167, A230197, A230198, A230257.

Sequence in context: A308656 A178775 A124874 * A016459 A242309 A275663

Adjacent sequences: A230255 A230256 A230257 * A230259 A230260 A230261

Keyword

nonn,easy

Author

Mircea Merca, Oct 14 2013

Status

approved