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 A014679 G.f.: (1+x^3)^2/((1-x^2)*(1-x^3)*(1-x^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, 238, 247, 258, 266, 275, 286, 295, 305 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS PoincarĂ© series [or Poincare series] (or Molien series) for mod 2 cohomology of M_12. REFERENCES A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 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 A. Adem, Recent developments in the cohomology of finite groups, Notices Amer. Math. Soc., 44 (1997), 806-812. Alejandro Adem; John Maginnis; James R. Milgram, The geometry and cohomology of the Mathieu group M_12, J. Algebra 139 (1991), no. 1, 90-133. Index entries for 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 ) / ( (1-x^4)*(1-x^6)*(1-x^7)). G.f.: (1-x+x^2)^2/((1-x)^3*(1+x^2)(1+x+x^2)). a(n)=n^2/12+n/4+13/36-A057077(n)/4+4*A099837(n+3)/9. - 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(n-1)- 2*a(n-2)+3*a(n-3)-3*a(n-4)+2*a(n-5)-2*a(n-6)+a(n-7). - Harvey P. Dale, Apr 10 2012 MAPLE (1+x^3)^2/((1-x^2)*(1-x^3)*(1-x^4)); MATHEMATICA CoefficientList[Series[(1+x^3)^2/((1-x^2)*(1-x^3)*(1-x^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 *) PROG (MAGMA) I:=[1, 0, 1, 3, 2, 3, 6]; [n le 7 select I[n] else 2*Self(n-1)- 2*Self(n-2)+3*Self(n-3)-3*Self(n-4)+2*Self(n-5)-2*Self(n-6)+Self(n-7): n in [1..60]]; // Vincenzo Librandi, Jul 19 2015 (PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 1, -2, 2, -3, 3, -2, 2]^n*[1; 0; 1; 3; 2; 3; 6])[1, 1] \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Sequence in context: A281667 A214297 A022472 * A208454 A187499 A187501 Adjacent sequences:  A014676 A014677 A014678 * A014680 A014681 A014682 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified July 23 14:36 EDT 2019. Contains 325255 sequences. (Running on oeis4.)