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A008611
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a(n) = a(n-3) + 1, with a(0)=a(2)=1, a(1)=0.
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19
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1, 0, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 15, 14, 15, 16, 15, 16, 17, 16, 17, 18, 17, 18, 19, 18, 19, 20, 19, 20, 21, 20, 21, 22, 21, 22, 23, 22, 23, 24, 23, 24, 25, 24, 25, 26, 25, 26, 27, 26, 27, 28
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Molien series of 2-dimensional representation of cyclic group of order 3 over GF(2).
One step back, two steps forward.
The crossing number of the graph C(n, {1,3}), n >= 8, is [n/3] + n mod 3, which gives this sequence starting at the first 4. [Yang Yuansheng et al.]
A Chebyshev transform of A078008. The g.f. is the image of (1-x)/(1-x-2x^2) (g.f. of A078008) under the Chebyshev transform A(x)-> 1/(1+x^2))A(x/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004
A047878 is an essentially identical sequence. - Anton Chupin, Oct 24 2009
Rhyme scheme of Dante Alighieri's "Divine Comedy." - David Gaita, Feb 11 2011
A194960 results from deleting the first four terms of A008611. Note that deleting the first term or first four terms of A008611 leaves a concatenation of segments (n, n+1, n+2); for related concatenations, see
A008619, (n,n+1) after deletion of first term;
A053737, (n,n+1,n+2,n+3) beginning with n=0;
A053824, (n to n+4) beginning with n=0. [From Clark Kimberling, Sep 7 2011]
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REFERENCES
| D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 103.
Yang Yuansheng et al., The crossing number of C(n; {1,3}), Discr. Math. 289 (2004), 107-118.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 447
G. P. Michon, Counting Polyhedra
Index entries for Molien series
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FORMULA
| a(n) = a(n-3)+1 = (n-1)-2*floor[(n-1)/3]. G.f.: (1+x^2+x^4)/(1-x^3)^2
After the initial term, has form {n, n+1, n+2} for n=0, 1, 2, ...
a(n)=sum{k=0..n, (-1)^floor(2(k-2)/3) }; a(n)=4sqrt(3)cos(2*pi*n/3+pi/6)/9+(n+1)/3. - Paul Barry (pbarry(AT)wit.ie), Mar 18 2004
G.f. : (1-x+x^2)/(1-x-x^3+x^4); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)*A078008(n-2k)*(-1)^k}. - Paul Barry (pbarry(AT)wit.ie), Oct 15 2004
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MATHEMATICA
| With[{nn=30}, Riffle[Riffle[Range[nn], Range[0, nn-1]], Range[nn], 3]] (* or *) RecurrenceTable[{a[0]==a[2]==1, a[1]==0, a[n]==a[n-3]+1}, a, {n, 90}] (* From Harvey P. Dale, Nov 06 2011 *)
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PROG
| (MAGMA) [(n-1)-2*Floor((n-1)/3): n in [0..90]]; // Vincenzo Librandi, Aug 21 2011
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CROSSREFS
| Cf. A058207, A058788.
Sequence in context: A033667 A033923 A116939 * A025798 A161064 A070086
Adjacent sequences: A008608 A008609 A008610 * A008612 A008613 A008614
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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