A230149 The number of multinomial coefficients over partitions with value equal to 5.

0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 3, 3, 2, 3, 4, 4, 4, 3, 5, 5, 5, 5, 5, 6, 6, 6, 7, 6, 7, 7, 8, 8, 7, 8, 9, 9, 9, 8, 10, 10, 10, 10, 10, 11, 11, 11, 12, 11, 12, 12, 13, 13, 12, 13, 14, 14, 14, 13, 15, 15, 15, 15, 15, 16, 16, 16, 17, 16, 17, 17, 18, 18, 17

Offset

1,9

Comments

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=5 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = floor((1/4)*(n-1)) +floor((1/5)*(n-1)) -floor((1/5)*n).

a(n) = a(n-4) + a(n-5) - a(n-9). - Charles R Greathouse IV, Oct 11 2013

G.f.: x^6*(1+x+x^2+2*x^3)/((1+x)*(1-x)^2*(1+x^2)*(1+x+x^2+x^3+x^4)). - Bruno Berselli, Oct 11 2013

Example

The number 11 has two partitions such that a(10)=5: 1+1+1+1+7 and 2+2+2+2+3.

Maple

seq(floor((n-1)*(1/4))+floor((n-1)*(1/5))-floor((1/5)*n), n=1..50)

Mathematica

CoefficientList[Series[x^5 (1 + x + x^2 + 2 x^3)/((1 + x) (1 - x)^2 (1 + x^2) (1 + x + x^2 + x^3 + x^4)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 11 2013 *)

Prog

(PARI) a(n)=(n-1)\4-(n%5==0) \\ Charles R Greathouse IV, Oct 11 2013

Crossrefs

Sequence in context: A056812 A210721 A082533 * A050373 A306433 A308174

Adjacent sequences: A230146 A230147 A230148 * A230150 A230151 A230152

Keyword

nonn,easy

Author

Mircea Merca, Oct 11 2013

Extensions

More terms from Bruno Berselli, Oct 11 2013

G.f. adapted to the offset from Vincenzo Librandi, Oct 11 2013

Status

approved