OFFSET
0,3
COMMENTS
Number of partitions of n into parts 1, 2, 3 and 5. - David Neil McGrath, Sep 15 2014
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,2,3,5).
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 29).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 239
Atsuto Seko, Atsushi Togo, and Isao Tanaka, Group-theoretical high-order rotational invariants for structural representations: Application to linearized machine learning interatomic potential, arXiv:1901.02118 [physics.comp-ph], 2019.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,0,0,-1,0,1,1,-1).
FORMULA
a(n) = round((n+3)*(2*n+9)*(n+9)/360).
G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)).
a(n) = -a(-11-n).
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-7) + a(n-9) + a(n-10) - a(n-11). - David Neil McGrath, Sep 15 2014
EXAMPLE
There are 6 partitions of 5 into parts 1,2,3 and 5. These are (5)(32)(311)(221)(2111)(11111). - David Neil McGrath, Sep 15 2014
MAPLE
1/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)); seq(coeff(series(%, x, n+1), x, n), n = 0..60); # modified by G. C. Greubel, Sep 08 2019
MATHEMATICA
LinearRecurrence[{1, 1, 0, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20}, 60] (* Harvey P. Dale, Feb 25 2015 *)
PROG
(PARI) a(n)=round((n+3)*(2*n+9)*(n+9)/360)
(Magma) [Round((n+3)*(2*n+9)*(n+9)/360): n in [0..60]]; // Vincenzo Librandi, Jun 23 2011
(Sage) [round((n+3)*(2*n+9)*(n+9)/360) for n in (0..60)] # G. C. Greubel, Sep 08 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved