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A092812
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Number of closed walks on the 4-cube.
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5
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1, 4, 40, 544, 8320, 131584, 2099200, 33562624, 536903680, 8590065664, 137439477760, 2199025352704, 35184380477440, 562949986975744, 9007199388958720, 144115188612726784, 2305843011361177600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| With interpolated zeros this has a(n)=(6*0^n + 4^n + (-4)^n + 4*2^n + 4*(-2)^n)/16 and counts closed walks of length n at a vertex of the 4-cube [Typo corrected by Alexander R. Povolotsky (pevnev(AT)juno.com), May 26 2008]
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REFERENCES
| Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
G. R. Franssens, On a number pyramid related to the binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1.
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FORMULA
| G.f.: (1-16*x+24*x^2)/((1-4*x)*(1-16*x)).
a(n) = 3*0^n/8+16^n/8+4^n/2.
E.g.f.: cosh^4(x). O.g.f.: 1/(1-4*1*x/(1-3*2*x/(1-2*3*x/(1-1*4*x)))) (continued fraction). - Peter Bala (pbala(AT)toucansurf.com), Nov 13 2006
(-1)^n*a(n)=Sum_{k, 0<=k<=n} A086872(n,k)*(-5)^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2007
a(0)=1, a(1)=4, a(2)=40, a(n)=20*a(n-1)-64*a(n-2) [From Harvey P. Dale, Aug 23 2011]
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MATHEMATICA
| CoefficientList[Series[(1-16x+24x^2)/((1-4x)(1-16x)), {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{20, -64}, {4, 40}, 30]] (* From Harvey P. Dale, Aug 23 2011 *)
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PROG
| (MAGMA) [3*0^n/8+16^n/8+4^n/2: n in [0..30]]; // Vincenzo Librandi, May 31 2011
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CROSSREFS
| Essentially the same as A075878. - Kang Seonghoon (lifthrasiir(AT)gmail.com), Oct 09 2008
Cf. A026244, A081294, A054879, A121822.
Cf. A075878. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 08 2008]
Sequence in context: A034385 A074637 A075878 * A196867 A128573 A052675
Adjacent sequences: A092809 A092810 A092811 * A092813 A092814 A092815
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 11 2004
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