A025768 - 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_