A230128 The number of multinomial coefficients over partitions with value equal to 4.

0, 0, 0, 0, 1, 1, 2, 1, 2, 3, 3, 2, 4, 4, 4, 4, 5, 5, 6, 5, 6, 7, 7, 6, 8, 8, 8, 8, 9, 9, 10, 9, 10, 11, 11, 10, 12, 12, 12, 12, 13, 13, 14, 13, 14, 15, 15, 14, 16, 16, 16, 16, 17, 17, 18, 17, 18, 19, 19, 18, 20, 20, 20, 20, 21, 21, 22, 21, 22, 23, 23, 22, 24

Offset

1,7

Comments

The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=4 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 (0,0,1,1,0,0,-1).

Formula

a(n) = floor((1/3)*(n-1)) + floor((1/4)*(n-1)) - floor((1/4)*n).

a(n) = a(n-3)+a(n-4)-a(n-7). G.f.: x^5*(2*x^2+x+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^2+x+1)). - Colin Barker, Mar 06 2014

Example

The number 10 has three partitions such that a(10)=4: 1+1+1+7, 1+3+3+3 and 2+2+2+4.

Maple

seq(floor((n-1)*(1/3))+floor((n-1)*(1/4))-floor((1/4)*n), n=1..50)

Mathematica

Table[Floor[(1/3) (n-1)] + Floor[(1/4) (n-1)] - Floor[(1/4) n], {n, 1, 100}] (* Vincenzo Librandi, Oct 11 2013 *)

Prog

(Magma) [Floor((1/3)*(n-1))+Floor((1/4)*(n-1))-Floor((1/4)*n): n in [1..100]]; // Vincenzo Librandi, Oct 11 2013

Crossrefs

Cf. A230149, A230167, A230197, A230198, A230257, A230258.

Sequence in context: A172089 A057475 A024376 * A342095 A340828 A123265

Adjacent sequences: A230125 A230126 A230127 * A230129 A230130 A230131

Keyword

nonn,easy

Author

Mircea Merca, Oct 10 2013

Extensions

More terms from Vincenzo Librandi, Oct 11 2013

Status

approved