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 A025768 Expansion of 1/((1-x)*(1-x^3)*(1-x^7)). 0
 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, 27, 28, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 54, 56, 58, 61, 63, 65, 68, 71, 73, 76, 79, 81, 84, 87, 90, 93, 96 (list; graph; refs; listen; history; text; internal format)
 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. 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 Sequence in context: A319922 A289139 A094838 * A000929 A029146 A029053 Adjacent sequences:  A025765 A025766 A025767 * A025769 A025770 A025771 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 18 18:20 EST 2018. Contains 317324 sequences. (Running on oeis4.)