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A057979
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a(n) = 1 for even n and (n-1)/2 for odd n.
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12
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1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 19, 1, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 34, 1, 35, 1, 36, 1, 37, 1, 38, 1, 39, 1, 40, 1, 41, 1, 42, 1, 43, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| a(n) = b(n)/c(n) where b(n) = A001405(n+1)-A001405(n), c(n) = GCD[A001405(n+1), A001405(n)]
Also the minimal number of disjoint edge-paths into which the complete graph on n edges can be partitioned - Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 19 2001
For n>=2, number of partitions of n-2 into parts that are distinct mod 2. - Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 06 2006
Sequence starting with a(3) obeys the rule "smallest positive value such that the ordered pair a(n-1),a(n) has not occurred previously", or the rule "smallest positive value such that the ratio a(n-1)/a(n) has not occurred previously". The same subsequence has its ordinal transform equal to itself, shifted left. (The ordinal transform has as its n-th term the number of values in a(1),...,a(n) that are equal to a(n).) - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 13 2006
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FORMULA
| a(n) = (n+3)/4+(1-n)*(-1)^n/4 - Paul Barry (pbarry(AT)wit.ie), Mar 21 2003, corrected by Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 25 2007
a(n) =(a(n-2)+a(n-3))/a(n-1).
G.f. : (1-x^2+x^3)/((1+x)^2(1-x)^2); a(n)=2a(n-2)-a(n-4); a(n)=0^n+sum{k=0..floor((n-2)/2), binomial(n-k-2, k)binomial(1, n-2k-2)}. - Paul Barry (pbarry(AT)wit.ie), Oct 21 2004
a(n)=gcd(n-1, floor((n-1)/2)) - Paul Barry (pbarry(AT)wit.ie), May 02 2005
a(n)=binomial((2n-3)/4-(-1)^n/4,(1-(-1)^n)/2); - Paul Barry (pbarry(AT)wit.ie), Jun 29 2006
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EXAMPLE
| n=13, C(13,6)-C(12,6)=792, GCD[C(13,6),C(12,6)]=132, the quotient is 6=Floor[13/2]; n=12 C(12,6)-C(11,5)=924-462=462,GCD[C(12,6),C(11,5)]=462, the quotient is 1.
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MATHEMATICA
| With[{no=45}, Riffle[Table[1, {no}], Range[0, no-1]]] (* From Harvey P. Dale, Feb 18 2011 *)
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CROSSREFS
| Cf. A001405, A007879, A059222, A000035, A027656, A037952.
Cf. A067992.
Sequence in context: A077610 A177815 A007879 * A152271 A133622 A158416
Adjacent sequences: A057976 A057977 A057978 * A057980 A057981 A057982
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 13 2000
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