

A014679


G.f.: (1+x^3)^2/((1x^2)*(1x^3)*(1x^4)).


1



1, 0, 1, 3, 2, 3, 6, 6, 7, 10, 11, 13, 16, 17, 20, 24, 25, 28, 33, 35, 38, 43, 46, 50, 55, 58, 63, 69, 72, 77, 84, 88, 93, 100, 105, 111, 118, 123, 130, 138, 143, 150, 159, 165, 172, 181, 188, 196, 205, 212, 221, 231
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OFFSET

0,4


COMMENTS

Poincare series (or Molien series) for mod 2 cohomology of M_12.


REFERENCES

A. Adem, Recent developments in the cohomology of finite groups, Notices Amer. Math. Soc., 44 (1997),806812.
Alejandro Adem; John Maginnis; James R. Milgram, The geometry and cohomology of the Mathieu group M_12, J. Algebra 139 (1991), no. 1, 90133.
A. Adem and R. J. Milgram, Cohomology of Finite Groups, SpringerVerlag, 2nd. ed., 2004; p. 255, Theorem 3.20, where the series is given in the form GF_2 (see formula line).


LINKS

T. D. Noe, Table of n, a(n) for n=0..1000
Index to sequences with linear recurrences with constant coefficients, signature (2,2,3,3,2,2,1).


FORMULA

Can also be written as GF_2 = (1 + x^2 + 3*x^3 + x^4 + 3*x^5 + 4*x^6 + 2*x^7 + 4*x^8 + 3*x^9 + x^10 + 3*x^11 + x^12 + x^14 ) / ( (1x^4)*(1x^6)*(1x^7)).
G.f.: (1x+x^2)^2/((1x)^3*(1+x^2)(1+x+x^2)). a(n)=n^2/12+n/4+13/36A057077(n)/4+4*A099837(n+3)/9. [From R. J. Mathar, Jan 11 2009]
a(0)=1, a(1)=0, a(2)=1, a(3)=3, a(4)=2, a(5)=3, a(6)=6, a(n)= 2*a(n1) 2*a(n2)+3*a(n3)3*a(n4)+2*a(n5)2*a(n6)+a(n7) [From Harvey P. Dale, Apr 10 2012]


MAPLE

(1+x^3)^2/((1x^2)*(1x^3)*(1x^4));


MATHEMATICA

CoefficientList[Series[(1+x^3)^2/((1x^2)*(1x^3)*(1x^4)), {x, 0, 60}], x] (* Harvey P. Dale, Mar 17 2011 *)
LinearRecurrence[{2, 2, 3, 3, 2, 2, 1}, {1, 0, 1, 3, 2, 3, 6}, 60] (* Harvey P. Dale, Apr 10 2012 *)


CROSSREFS

Sequence in context: A058691 A214297 A022472 * A208454 A187499 A187501
Adjacent sequences: A014676 A014677 A014678 * A014680 A014681 A014682


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



