0,3

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115, row m=5 of Q(m,n) table.

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 2.

Gerzson Keri and Patric R. J. Ostergard, The Number of Inequivalent (2R+3,7)R Optimal Covering Codes, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.7.

T. D. Noe, Table of n, a(n) for n=0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 354

Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.

B. Kisacanin, Mathematical Problems and Proofs, Plenum, New York, 1998, pp. 71-72.

Jon Perry, More Partition Function

G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)).

a(n)=1+(a(n-2)+a(n-3)+a(n-4))-(a(n-6)+(2*a(n-7))+a(n-8))+(a(n-10)+a(n-11)+a(n-12))-a(n-14) - Norman J. Meluch (norm(AT)iss.gm.com), Mar 09 2000

Let a1(n)=sum(i=0, floor(n/3), 1+ceil((n-3*i-1)/2)), a2(n)=sum(i=0, floor(n/4), 1+ceil((n-4*i-1)/2)+a1(n-4*i-3)), then a(n)=sum(i=0, floor(n/5), 1+ceil((n-5*i-1)/2)+a1(n-5*i-3)+a2(n-5*i-4)). - Jon Perry (perry(AT)globalnet.co.uk), Jun 27 2003

(n choose 5)_q=(q^n-1)*(q^(n-1)-1)*(q^(n-2)-1)*(q^(n-3)-1)*(q^(n-4)-1)/((q^5-1)*(q^4-1)*(q^3-1)*(q^2-1)*(q-1))

(5 choose 5)_q = 1, (6 choose 5)_q = q^5 + q^4 + q^3 + q^2 + q + 1, (7 choose 5)_q = q^10 + q^9 + 2*q^8 + 2*q^7 + 3*q^6 + 3*q^5 + 3*q^4 + 2*q^3 + 2*q^2 + q + 1, (8 choose 5)_q = q^15 + q^14 + 2*q^13 + 3*q^12 + 4*q^11 + 5*q^10 + 6*q^9 + 6*q^8 + 6*q^7 + 6*q^6 + 5*q^5 + 4*q^4 + 3*q^3 + 2*q^2 + q + 1 so the coefficient of q^0 converges to 1, q^1 to 1, q^2 to 2 and so on.

with(combstruct):ZL6:=[S, {S=Set(Cycle(Z, card<6))}, unlabeled]:seq(count(ZL6, size=n), n=0..52); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007

(Maple) a := n -> (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..52); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]

B:=[S, {S = Set(Sequence(Z, 1 <= card), card <=5)}, unlabelled]: seq(combstruct[count](B, size=n), n=0..52); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2009]

CoefficientList[ Series[ 1/((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^5)), {x, 0, 60} ], x ]

a(n)=A008284(n+5, 5), n >= 0.

Cf. A008619, A001400, A001399.

First differences of A002622.

Adjacent sequences: A001398 A001399 A001400 this_sequence A001402 A001403 A001404

Sequence in context: A062684 A033485 A026811 this_sequence A008628 A038499 A118199

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

Additional comments from Michael Somos and Branislav Kisacanin (branislav.kisacanin(AT)delphiauto.com)