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A006234
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n*3^(n-4).
(Formerly M3496)
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25
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1, 4, 15, 54, 189, 648, 2187, 7290, 24057, 78732, 255879, 826686, 2657205, 8503056, 27103491, 86093442, 272629233, 860934420, 2711943423, 8523250758, 26732013741, 83682825624, 261508830075, 815907549834, 2541865828329
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| For n >= 1 a(n) is also the determinant of the n-3 X n-3 matrix with 4's on the diagonal and 1's elsewhere. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 06 2001
a(n+3)=det(M(n)) where M(n) is the n X n matrix with m(i,i)=4, m(i,j)=i/j for i != j. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003
Main diagonal of array defined by m(1,j)=j; m(i,1)=i and m(i,j)=m(i-1,j)+2*m(i-1,j-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 13 2003
a(n+3) is the number of words of length n on {A, B, C, D} with no D appearing anywhere to the right of an A. - Rob Pratt (Rob.Pratt(AT)sas.com), Aug 04 2004
Number of spanning trees in the book graph of order n-2, i.e., S_{n-2} X P_2 (S_k = the star graph on k nodes) (conjectured).
a(n+3) = sum of the n-th row of A112626. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2006
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REFERENCES
| G. Kreweras, Complexite et circuits Euleriens dans la sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 3..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to linear recurrences with constant coefficients
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Spanning Tree
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FORMULA
| G.f.: (1-2x)/(1-3x)^2 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003
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MAPLE
| A006234:=-(-1+2*z)/(3*z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (MAGMA) [ n*3^(n-4): n in [3..30] ]; // Vincenzo Librandi, Aug 19 2011
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CROSSREFS
| Binomial transform of A001792.
Cf. A036290, A050914.
Sequence in context: A071719 A164619 A090326 * A094821 A071723 A001559
Adjacent sequences: A006231 A006232 A006233 * A006235 A006236 A006237
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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