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A230128 The number of multinomial coefficients over partitions with value equal to 4. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A123265 A104345 A244516

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

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)