A230257 The number of multinomial coefficients over partitions with value equal to 9.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 5, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 8, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 12, 12, 11

Offset

1,17

Comments

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=9 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..99.

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

Formula

a(n) = floor((n-1)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n).

G.f.: x^10*(2*x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^2+x+1)*(x^4+1)*(x^6+x^3+1)). - Colin Barker, Mar 06 2014

Example

The number 25 has three partitions such that a(25)=8: 1+1+1+1+1+1+1+1+17, 1+3+3+3+3+3+3+3+3 and 2+2+2+2+2+2+2+2+9.

Maple

seq(floor((n-1)/8)+floor((n-1)/9)-floor(n/9), n=1..99);

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2}, 100] (* Harvey P. Dale, Mar 20 2016 *)

Crossrefs

A230128, A230149, A230167, A230197, A230198, A230258.

Sequence in context: A025851 A343911 A125688 * A060508 A029404 A029417

Adjacent sequences: A230254 A230255 A230256 * A230258 A230259 A230260

Keyword

nonn,easy

Author

Mircea Merca, Oct 14 2013

Extensions

Typos in formula and Maple code fixed by Colin Barker, Mar 06 2014

Status

approved