OFFSET
0,4
COMMENTS
(x^4+x^5+x^6+2*x^7+x^8+x^9+x^10) / ((1-x^4)*(1-x^6)*(1-x^7)) is the Poincaré series [or Poincare series] (or Molien series) for (H^*(Q)⊗ St)^(GL_3(F_2)). This gives the same sequence but prefixed by four 0's.
a(n) is the number of nonnegative integer solutions to the equation: x + y + z = n such that y >= 2*x and z >= 2*y. - Geoffrey Critzer, Jul 09 2013
Number of partitions of n into parts 1, 3, and 7. - Joerg Arndt, Jul 10 2013
REFERENCES
A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 259.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,3,7).
LINKS
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 46.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 0, 0, 1, -1, 0, -1, 1).
FORMULA
a(n) = round((n+3)*(n+8)/42).
a(n)= +a(n-1) +a(n-3) -a(n-4) +a(n-7) -a(n-8) -a(n-10) +a(n-11). - R. J. Mathar, Aug 21 2014
EXAMPLE
a(6)=3 because we have: 0+0+6 = 0+1+5 = 0+2+4. - Geoffrey Critzer, Jul 09 2013
MATHEMATICA
nn=58; CoefficientList[Series[1/(1-x)/(1-x^3)/(1-x^7), {x, 0, nn}], x] (* Geoffrey Critzer, Jul 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved