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Search: id:A054879
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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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+0
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; listen)
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OFFSET
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0,2
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COMMENT
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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
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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
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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
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G.f.: 1/4*1/(1-9*x)+3/4*1/(1-x). a(n)=(3^(2*n)+3)/4.
a(n) = Sum_{k, 0<=k<=n} 3^k*4^(n-k)*A121314(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 26 2006
a(n) = Sum_{k, 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_{k, 0<=k<=n} A086872(n,k)*(-4)^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2007
a(n)=9*a(n-1)-6 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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EXAMPLE
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For n=2, a(2)=9*1-6=3; n=3, a(3)=9*3-6=21; n=4, a(4)=9*21-6=183 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
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CROSSREFS
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Cf. A081294, A092812, A121822.
A158301 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 15 2009]
Sequence in context: A118353 A046637 A132805 this_sequence A131763 A006199 A083063
Adjacent sequences: A054876 A054877 A054878 this_sequence A054880 A054881 A054882
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KEYWORD
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nonn,walk,new
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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