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%I #19 Feb 10 2024 12:07:06
%S 0,0,0,0,0,2,2,4,4,7,7,10,10,15,14,20,19,25,24,31,31,39,37,45,44,55,
%T 53,63,61,72,71,83,81,94,91,105,103,118,115,130,128,144,141,158,155,
%U 174,170,188,185,205,202,222,218,239,235,258,254,277,272,295,292,317,312,337
%N The number of multinomial coefficients over partitions with value equal to 6.
%C The number of multinomial coefficients such that multinomial(t_1+t_2+..._+t_n,t_1,t_2,...,t_n)=6 and t_1+2*t_2+...+n*t_n=n, where t_1, t_2, ... , t_n are nonnegative integers.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1,1,0,0,-1,-1,-1,0,0,0,1).
%F a(n) = floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)).
%F G.f.: x^6*(2*x^9-2*x^6-3*x^5-5*x^4-4*x^3-4*x^2-2*x-2) / ((x-1)^3*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - _Colin Barker_, Oct 15 2013
%e The number 8 has four partitions such that a(8)=6: 1+1+1+1+1+3, 1+1+3+3, 1+2+5 and 1+3+4.
%p seq(floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)),n=1..50)
%Y Cf. A036040, A230128, A230149, A230197, A230198, A230257, A230258.
%K nonn,easy
%O 1,6
%A _Mircea Merca_, Oct 11 2013
%E More terms from _Colin Barker_, Mar 06 2014