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A230257 The number of multinomial coefficients over partitions with value equal to 9. 5
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 (list; graph; refs; listen; history; text; internal format)
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)*(1/8))+floor((n-1)*(1/9))-floor((1/9)*n)), 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: A194824 A025851 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

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Last modified August 4 13:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)