Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Sep 30 2023 12:13:40
%S 1,1,1,2,2,2,3,4,4,5,6,6,7,8,9,10,11,12,13,14,15,17,18,19,21,22,23,25,
%T 27,28,30,32,33,35,37,39,41,43,45,47,49,51,54,56,58,61,63,65,68,71,73,
%U 76,79,81,84,87,90,93,96
%N Expansion of 1/((1-x)*(1-x^3)*(1-x^7)).
%C (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.
%C 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
%C Number of partitions of n into parts 1, 3, and 7. - _Joerg Arndt_, Jul 10 2013
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 259.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,3,7).
%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; see page 46.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1, 0, 0, 1, -1, 0, -1, 1).
%F a(n) = round((n+3)*(n+8)/42).
%F 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
%e a(6)=3 because we have: 0+0+6 = 0+1+5 = 0+2+4. - _Geoffrey Critzer_, Jul 09 2013
%t nn=58;CoefficientList[Series[1/(1-x)/(1-x^3)/(1-x^7),{x,0,nn}],x] (* _Geoffrey Critzer_, Jul 09 2013 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_