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A230198 The number of multinomial coefficients over partitions with value equal to 8. 5
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 6, 6, 6, 6, 6, 5, 6, 7, 7, 7, 7, 7, 7, 6, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 9, 10, 10, 10, 10, 10, 11, 11, 10, 11, 11, 11, 11, 12, 12, 12, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

COMMENTS

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=8 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..88.

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

FORMULA

a(n) = floor((n-1)*(1/7))+floor((n-1)*(1/8))-floor((1/8)*n).

G.f.: x^9*(2*x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)*(x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Oct 14 2013

EXAMPLE

The number 22 has three partitions such that a(22)=8: 1+1+1+1+1+1+1+15, 1+3+3+3+3+3+3+3 and 2+2+2+2+2+2+2+8.

MAPLE

seq(floor((n-1)*(1/7))+floor((n-1)*(1/8))-floor((1/8)*n), n=1..75)

MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2}, 100] (* Harvey P. Dale, Aug 22 2019 *)

CROSSREFS

Cf. A230128, A230149, A230167, A230197, A230257, A230258.

Sequence in context: A243866 A110102 A255472 * A024939 A024937 A143977

Adjacent sequences:  A230195 A230196 A230197 * A230199 A230200 A230201

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Oct 11 2013

EXTENSIONS

More terms from Colin Barker, Mar 06 2014

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)