A008779 Number of n-dimensional partitions of 5.
1, 7, 24, 59, 120, 216, 357, 554, 819, 1165, 1606, 2157, 2834, 3654, 4635, 5796, 7157, 8739, 10564, 12655, 15036, 17732, 20769, 24174, 27975, 32201, 36882, 42049, 47734, 53970, 60791, 68232, 76329, 85119, 94640, 104931, 116032, 127984, 140829, 154610, 169371
Offset: 0
References
- G. E. Andrews, The Theory of Partitions, Add.-Wes. '76, p. 190.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, J. Integer Seqs., Vol. 6, 2003.
- Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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GAP
List([0..45], n-> (n+1)*(n^3 + 21*n^2 + 38*n + 24)/24); # G. C. Greubel, Sep 11 2019
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Magma
[(n+1)*(n^3+21*n^2+38*n+24)/24: n in [0..45]]; // Vincenzo Librandi, May 21 2015
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Magma
I:=[1,7,24,59,120]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..45]]; // Vincenzo Librandi, May 21 2015
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Maple
seq(1+6*n+11*binomial(n,2)+7*binomial(n,3)+binomial(n,4), n=0..45);
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Mathematica
CoefficientList[Series[(1+2*x-x^2-x^3)/(1-x)^5, {x,0,45}], x] (* Vincenzo Librandi, May 21 2015 *) LinearRecurrence[{5,-10,10,-5,1}, {1,7,24,59,120}, 46] (* G. C. Greubel, Sep 11 2019 *) -
PARI
Vec((-1+x^3+x^2-2*x)/(x-1)^5 + O(x^45)) \\ Altug Alkan, Jan 07 2016
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Sage
[(n+1)*(n^3 + 21*n^2 + 38*n + 24)/24 for n in (0..45)] # G. C. Greubel, Sep 11 2019
Formula
G.f.: (1 +2*x -x^2 -x^3)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009
a(n) = (n+1)*(n^3 + 21*n^2 + 38*n + 24)/24. - M. F. Hasler, Sep 15 2009
a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5). - Vincenzo Librandi, May 21 2015
E.g.f.: (24 + 144*x + 132*x^2 + 28*x^3 + x^4)*exp(x)/24. - G. C. Greubel, Sep 11 2019
Extensions
More terms from Vincenzo Librandi, May 21 2015
Comments