A230167 The number of multinomial coefficients over partitions with value equal to 6.

0, 0, 0, 0, 0, 2, 2, 4, 4, 7, 7, 10, 10, 15, 14, 20, 19, 25, 24, 31, 31, 39, 37, 45, 44, 55, 53, 63, 61, 72, 71, 83, 81, 94, 91, 105, 103, 118, 115, 130, 128, 144, 141, 158, 155, 174, 170, 188, 185, 205, 202, 222, 218, 239, 235, 258, 254, 277, 272, 295, 292, 317, 312, 337

Offset

1,6

Comments

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=6 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..64.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,0,0,0,1).

Formula

a(n) = floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)).

G.f.: x^6*(2*x^9-2*x^6-3*x^5-5*x^4-4*x^3-4*x^2-2*x-2) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Oct 15 2013

Example

The number 8 has four partitions such that a(8)=6: 1+1+1+1+1+3, 1+1+3+3, 1+2+5 and 1+3+4.

Maple

seq(floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)), n=1..50)

Crossrefs

Cf. A036040, A230128, A230149, A230197, A230198, A230257, A230258.

Sequence in context: A348543 A085893 A341950 * A060028 A341951 A182410

Adjacent sequences: A230164 A230165 A230166 * A230168 A230169 A230170

Keyword

nonn,easy

Author

Mircea Merca, Oct 11 2013

Extensions

More terms from Colin Barker, Mar 06 2014

Status

approved