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A004525
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One even followed by three odd.
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9
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0, 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 13, 14, 15, 15, 15, 16, 17, 17, 17, 18, 19, 19, 19, 20, 21, 21, 21, 22, 23, 23, 23, 24, 25, 25, 25, 26, 27, 27, 27, 28, 29, 29, 29, 30, 31, 31, 31, 32, 33, 33, 33, 34, 35, 35, 35, 36, 37, 37, 37
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n+1) is the composition length of the n-th symmetric power of the natural representation of a finite subgroup of SL(2,C) of type E_6 (binary tetrahedral group). - Paul Boddington (psb(AT)maths.warwick.ac.uk), Oct 23 2003
(1 + x + x^2 + x^3 + x^4 + x^5) / ( (1-x^3)*(1- x^4)) is the Poincare series (or Molien series) for H^*(GL_2(F_3)).
The Fi1 and Fi2 sums, see A180662 for the definition of these sums, of triangle A101950 equal the terms of this sequence without the first term. [Johannes W. Meijer, Aug 06 2011]
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REFERENCES
| A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 247.
Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, 1999.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for two-way infinite sequences
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FORMULA
| a(n) = a(n-1)-a(n-2)+a(n-3)+1 = n-A004524(n+1) - Henry Bottomley, Mar 08 2000
G.f.: x*(1-x+x^2)/((1-x)^2*(1+x^2)) = x*(1-x^6)/((1-x)*(1-x^3)*(1-x^4)).
a(n)=-a(-n).
a(n) = floor(n/4) + ceiling(n/4). See also A004396, one even followed by two odd and A002620, quarter-squares: floor(n/2)*ceiling(n/2). - Jonathan Vos Post, Mar 19 2006
a(n+1)=sum{k=0..n, (1+(-1)^comb(k+1,2))/2}; - Paul Barry, Mar 31 2008
E.g.f: A(x)=(x*exp(x)+sin(x))/2 [From Vladimir Kruchinin, Feb 20 2011]
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MAPLE
| A004525 := proc(n): floor(n/4) + ceil(n/4) end: seq(A004525(n), n=0..75); # [Johannes W. Meijer, Aug 06 2011]
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PROG
| (PARI) a(n)=n\4+(n+3)\4
(MAGMA) [Floor(n/4) + Ceiling(n/4): n in [0..70]]; // Vincenzo Librandi, Aug 07 2011
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CROSSREFS
| Cf. A004524.
Cf. A002620, A004396.
Sequence in context: A153161 A194171 * A049206 A194247 A084767 A137580
Adjacent sequences: A004522 A004523 A004524 * A004526 A004527 A004528
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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