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A054879
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Closed walks of length 2n along the edges of a cube based at a vertex.
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8
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1, 3, 21, 183, 1641, 14763, 132861, 1195743, 10761681, 96855123, 871696101, 7845264903, 70607384121, 635466457083, 5719198113741, 51472783023663, 463255047212961, 4169295424916643, 37523658824249781
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Starting with "3" = odd row sums of triangle A158301 terms. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 15 2009]
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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..1000
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
| a(n)=(3^(2*n)+3)/4.
G.f.: 1/4*1/(1-9*x)+3/4*1/(1-x).
a(n) = sum(0<=k<=n, 3^k*4^(n-k)*A121314(n,k) ). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 26 2006
E.g.f.: cosh^3(x). O.g.f.: 1/(1-3*1*x/(1-2*2*x/(1-1*3*x))) (continued fraction). - Peter Bala (pbala(AT)toucansurf.com), Nov 13 2006
(-1)^n*a(n)=sum(0<=k<=n, A086872(n,k)*(-4)^(n-k) ). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2007
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PROG
| (MAGMA) [(3^(2*n)+3)/4: n in [0..25]]; // Vincenzo Librandi, Jun 30 2011
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CROSSREFS
| Cf. A081294, A092812, A121822.
A158301 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 15 2009]
Sequence in context: A206397 A195105 A192946 * A131763 A006199 A083063
Adjacent sequences: A054876 A054877 A054878 * A054880 A054881 A054882
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KEYWORD
| nonn,walk
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AUTHOR
| Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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