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 A008637 Number of partitions of n into at most 8 parts. 5
 1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 230, 288, 352, 434, 525, 638, 764, 919, 1090, 1297, 1527, 1801, 2104, 2462, 2857, 3319, 3828, 4417, 5066, 5812, 6630, 7564, 8588, 9749, 11018, 12450, 14012, 15765, 17674, 19805, 22122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n>7: also number of partitions of n into parts <= 8: a(n)=A026820(n,8). [From Reinhard Zumkeller, Jan 21 2010] Molien series for finite Coxeter group of type A_8. Number of different distributions of n+36 identical balls in 8 boxes as x,y,z,p,q,m,n,h where 0= 0. a(n) = floor((-1)^n*((n+1)*(-1)^(floor((n+2)/3))+(2*n+3)*(-1)^(floor((n+1)/3))+(n+2)*(-1)^(floor(n/3)))/972+(n+2)*((-1)^n+1)*(-1)^(n/2)/512+(n+18)*(6*n^6+648*n^5+27018*n^4+545616*n^3+5481213*n^2+25163028*n+39226571)/1219276800+(n+1)*(n^2+53*n+826)*(-1)^n/36864+1/2). (See link.) - Tani Akinari, Oct 26 2012 a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-9) + a(n-11) + 2*a(n-12) + a(n-13) + a(n-15) - a(n-16) - a(n-17) - 2*a(n-18) - a(n-19) - a(n-20) + a(n-21) + a(n-23) + 2*a(n-24) + a(n-25) - a(n-27) - a(n-29) - a(n-31) + a(n-34) + a(n-35) - a(n-36). - David Neil McGrath, Apr 14 2015 a(n+8) = a(n) + A008636(n). - Ece Uslu, Esin Becenen, Jan 11 2016 EXAMPLE There are a(9)=29 partitions of 9 into parts less than or equal to 8. These are (81)(72)(711)(63)(621)(6111)(54)(531)(522)(5211)(51111)(441)(432)(4311)(4221)(42111)(411111)(333)(3321)(33111)(3222)(32211)(321111)(3111111)(22221)(222111)(2211111)(21111111)(111111111). - David Neil McGrath, Apr 14 2015 a(3) = 3 i.e. {1,2,3,4,5,7,8,9},{1,2,3,4,5,6,8,10},{1,2,3,4,5,6,7,11} Number of different distributions of 39 identical balls in 8 boxes as x,y,z,p,q,m,n,h where 0

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Last modified April 11 22:31 EDT 2021. Contains 342895 sequences. (Running on oeis4.)