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 A001401 Number of partitions of n into at most 5 parts. (Formerly M0642 N0237) 21
 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 84, 101, 119, 141, 164, 192, 221, 255, 291, 333, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1342, 1469, 1602, 1747, 1898, 2062, 2233, 2418, 2611, 2818, 3034, 3266, 3507, 3765, 4033, 4319 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = T_{r}(n) for r large, where T_{r}(n) = number of outcomes in which r indistinguishable dice yield a sum r+n-1. a(n) = coefficient of q^n in the expansion of (m choose 5)_q as m goes to infinity. - Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 21 2002 For n>4: also number of partitions of n into parts <= 5: a(n)=A026820(n,5). [From Reinhard Zumkeller, Jan 21 2010] Number of different distributions of n+15 identical balls in 5 boxes as x,y,z,p,q where 0 (Matrix(15, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=0..60); # Alois P. Heinz, Jul 31 2008 B:=[S, {S = Set(Sequence(Z, 1 <= card), card <=5)}, unlabelled]: seq(combstruct[count](B, size=n), n=0..52); # Zerinvary Lajos, Mar 21 2009 MATHEMATICA CoefficientList[ Series[ 1/((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^5)), {x, 0, 60} ], x ] a[n_] := IntegerPartitions[n, 5] // Length; Table[a[n], {n, 0, 52}] (* Jean-François Alcover, Jul 13 2012 *) PROG (PARI) a(n)=#partitions(n, , 5) \\ Charles R Greathouse IV, Sep 15 2014 CROSSREFS a(n) = A008284(n+5, 5), n >= 0. Cf. A008619, A001400, A001399, A008667 (first differences). First differences of A002622. Sequence in context: A062684 A033485 A026811 * A008628 A038499 A118199 Adjacent sequences:  A001398 A001399 A001400 * A001402 A001403 A001404 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Additional comments from Michael Somos and Branislav Kisacanin (branislav.kisacanin(AT)delphiauto.com) STATUS approved

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Last modified June 21 11:49 EDT 2018. Contains 305619 sequences. (Running on oeis4.)