A025768 Expansion of 1/((1-x)*(1-x^3)*(1-x^7)).

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

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

Table of n, a(n) for n=0..58.

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

Sequence in context: A319922 A289139 A094838 * A000929 A325358 A029146

Adjacent sequences: A025765 A025766 A025767 * A025769 A025770 A025771

Keyword

nonn

Author

N. J. A. Sloane

Status

approved