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Search: id:A054878
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| A054878 |
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Closed walks of length n along the edges of a tetrahedron based at a vertex. |
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+0
8
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| 1, 0, 3, 6, 21, 60, 183, 546, 1641, 4920, 14763, 44286, 132861, 398580, 1195743, 3587226, 10761681, 32285040, 96855123, 290565366, 871696101, 2615088300, 7845264903, 23535794706, 70607384121, 211822152360, 635466457083
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of closed walks of length n at a vertex of C_4, the cyclic graph on 4 nodes. 3*A015518(n)+A054878(n)=3^n. - Paul Barry (pbarry(AT)wit.ie), Feb 03 2004
Form the digraph with matrix A=[0,1,1,1;1,0,1,1;1,1,0,1;1,0,1,1]. A054878(n) corresponds to the (1,1) term of A^n. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
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FORMULA
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G.f.: 1/4*(3/(t+1)-1/(3*t-1)). a(n)=(3^n+(-1)^n*3)/4
E.g.f. (exp(3x)+3exp(-x))/4. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2003
Also: a(n)=3^n-a(n-1) with a(0)=0 - Labos E. (labos(AT)ana.sote.hu), Apr 26 2003
G.f.: (1-3x^2-2x^3)/(1-6x^2-8x^3-3x^4)=(1-3x^2-2x^3)/charpoly(adj(C_4)); a(n)=6a(n-2)+8a(n-3)+3a(n-4). - Paul Barry (pbarry(AT)wit.ie), Feb 03 2004
G.f. : (1-2x)/(1-2x-3x^2) a(n)=2a(n-1)+3a(n-2); a(n)=a(n-1)+5a(n-2)+3a(n-3). - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004
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CROSSREFS
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{a(n)/3} for n>0 is A015518.
Sequence in context: A063683 A098511 A112520 this_sequence A084567 A135686 A025229
Adjacent sequences: A054875 A054876 A054877 this_sequence A054879 A054880 A054881
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KEYWORD
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nonn,walk
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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