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Search: id:A047849
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| 1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 349526, 1398102, 5592406, 22369622, 89478486, 357913942, 1431655766, 5726623062, 22906492246, 91625968982, 366503875926, 1466015503702, 5864062014806, 23456248059222
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Counts closed walks of length 2n at a vertex of the cyclic graph on 6 nodes C_6. - Paul Barry (pbarry(AT)wit.ie), Mar 10 2004
A. A. Ivanov conjectures that the dimension of the universal embedding of the unitary dual polar space DSU(2n,4) is a(n). - J. Taylor (jt_cpp(AT)yahoo.com), Apr 02 2004.
Permutations with two fixed points avoiding 123 and 132.
Related to A024495(6n), A131708(6n+2), A024493(6n+4). First differences give A000302. - Paul Curtz (bpcrtz(AT)free.fr), Mar 25 2008
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LINKS
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B. N. Cooperstein and E. E. Shult, A note on embedding and generating dual polar spaces. Adv. Geom. 1 (2001), 37-48. See Conjecture 5.5.
T. Mansour and A. Robertson, Refined restricted permutations....
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FORMULA
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a(n) =(4^n+2)/3 =4a(n-1)-2 =5a(n-1)-4a(n-2) =2*A007583(n-1) =A002450(n)+1 - Henry Bottomley (se16(AT)btinternet.com), Aug 29 2000
With interpolated zeros, this is (-2)^n/6+2^n/6+(-1)^n/3+1/3. - Paul Barry (pbarry(AT)wit.ie), Aug 26 2003
a(n) = A007583(n) - A002450(n) = A001045(2n+1) - A001045(2n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 25 2004
Second binomial transform of A078008. Binomial transform of 1, 1, 3, 9, 81, .. (3^n/3+2*0^n/3). a(n)=A078008(2n). - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
G.f.: (1-3x)/((x-1)(4x-1)) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 06 2004
a(n) = Sum_{k, 0<=k<=n} 2^k*A121314(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 15 2006
a(n)=A002450(n)+1 - Artur Jasinski (grafix(AT)csl.pl), Jan 29 2007
a(n)=(A001045(2n+1)+1)/2; - Paul Barry (pbarry(AT)wit.ie), Dec 05 2007
For n>1, a(n) = 4*a(n-1) - 2 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 26 2007
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=4*a[n-1]+1 od: seq(a[n]+1, n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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MATHEMATICA
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a = {}; k = 1; Do[k = k + 2^(2x); AppendTo[a, k], {x, 0, 100}]; a - Artur Jasinski (grafix(AT)csl.pl), Jan 29 2007
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CROSSREFS
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n-th difference of a(n), a(n-1), ..., a(0) is 3^(n-1) for n=1, 2, 3, ...
Cf. A002450.
Adjacent sequences: A047846 A047847 A047848 this_sequence A047850 A047851 A047852
Sequence in context: A107244 A107246 A107247 this_sequence A107245 A073075 A101043
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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