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 A230167 The number of multinomial coefficients over partitions with value equal to 6. 5
 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, 53, 63, 61, 72, 71, 83, 81, 94, 91, 105, 103, 118, 115, 130, 128, 144, 141, 158, 155, 174, 170, 188, 185, 205, 202, 222, 218, 239, 235, 258, 254, 277, 272, 295, 292, 317, 312, 337 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS 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. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,0,0,0,1). FORMULA a(n)=floor((1/12)*(n-3)^2)+floor((n-1)*(1/5))+((1+(-1)^n)*(1/2))*floor((n-2)*(1/4)). 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 EXAMPLE 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. MAPLE 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) CROSSREFS Cf. A036040, A230128, A230149, A230197, A230198, A230257, A230258. Sequence in context: A287144 A085893 A341950 * A060028 A341951 A182410 Adjacent sequences:  A230164 A230165 A230166 * A230168 A230169 A230170 KEYWORD nonn,easy AUTHOR Mircea Merca, Oct 11 2013 EXTENSIONS More terms from Colin Barker, Mar 06 2014 STATUS approved

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)