A230198 The number of multinomial coefficients over partitions with value equal to 8.

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

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: A110102 A375603 A255472 * A024939 A024937 A378126

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