A230197 The number of multinomial coefficients over partitions with value equal to 7.

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

Offset

1,13

Comments

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=7 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..75.

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

Formula

a(n) = floor((n-1)*(1/6))+floor((n-1)*(1/7))-floor((1/7)*n).

G.f.: x^8*(2*x^5+x^4+x^3+x^2+x+1) / ((x-1)^2*(x+1)*(x^2-x+1)*(x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Oct 14 2013

Example

The number 19 has three partitions such that a(19)=3: 1+1+1+1+1+1+13, 1+3+3+3+3+3+3 and 2+2+2+2+2+2+7.

Maple

seq(floor((n-1)*(1/6))+floor((n-1)*(1/7))-floor((1/7)*n), n=1..75)

Crossrefs

Cf. A230128, A230149, A230167, A230198, A230257, A230258.

Sequence in context: A308342 A303399 A053597 * A094570 A225638 A332656

Adjacent sequences: A230194 A230195 A230196 * A230198 A230199 A230200

Keyword

nonn,easy

Author

Mircea Merca, Oct 11 2013

Status

approved