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Search: id:A028242
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| A028242 |
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Follow n by n-1. Also (essentially) Molien series of 2-dimensional quaternion group Q_8. |
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+0
25
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| 1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, 28, 30, 29, 31, 30, 32, 31, 33, 32, 34, 33, 35, 34, 36, 35, 37, 36, 38
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A two-way infinite sequences which is palindromic (up to sign). - Michael Somos, Mar 21, 2003
Number of permutations of [n+1] avoiding the patterns 123, 132, and 231 and having exactly one fixed point. Example: a(0) because we have 1; a(2)=2 because we have 213 and 321; a(3)=1 because we have 3214. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 17 2005
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REFERENCES
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D. Benson, Polynomial Invariants of Finite Groups, Cambridge, p. 23.
S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; see p. 15.
M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 97.
L. Smith, Polynomial Invariants of Finite Groups, A K Peters, 1995, p. 90.
T. Mansour and A. Robertson, Refined restricted permutations avoiding subsets of patterns of length three, Annals of Combinatorics, 6, 2002, 407-418; Theorem 3.3.
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LINKS
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Index entries for Molien series
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FORMULA
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Molien series is (1+x^6)/(1-x^4)^2.
a(n) = n-a(n-1) [with a(0) = 1] = A000035(n-1)+A004526(n) [noting that A004526 offset by 1 also satisfies a(n) = n-a(n-1) but with a(0) = 0]. - Henry Bottomley (se16(AT)btinternet.com), Jul 25 2001
G.f.: (1-x+x^2)/((1-x)(1-x^2)). a(2n)=n+1, a(2n+1)=n, a(-1-n)=-a(n). a(n)=a(n-1)+a(n-2)-a(n-3).
a(n) = floor(n/2) + 1 - n mod 2. a(2*k) = k+1, a(2*k+1) = k; A110657(n) = a(a(n)), A110658(n) = a(a(a(n))); a(n) = A109613(n)-A110654(n) = A110660(n)/A110654(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 05 2005
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MAPLE
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series((1+x^3)/(1-x^2)^2, x, 80);
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PROGRAM
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(PARI) a(n)=(n\2)-(n%2)+1
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CROSSREFS
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Partial sums give A004652. A030451(n)=A028242(n+1), n>0.
Sequence in context: A026238 A066136 A097140 this_sequence A030451 A029162 A005044
Adjacent sequences: A028239 A028240 A028241 this_sequence A028243 A028244 A028245
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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