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A006238 Complexity of (or spanning trees in) a 3 X n grid.
(Formerly M4986)
+0
4
1, 15, 192, 2415, 30305, 380160, 4768673, 59817135, 750331584, 9411975375, 118061508289, 1480934568960, 18576479568193, 233018797965135, 2922930580320960, 36664523428884015, 459910778352898337 (list; graph; listen)
OFFSET

1,2

COMMENT

a(n) is a divisibility sequence - m divides n implies that a(m) divides a(n). [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

G. Kreweras, Complexite et circuits Euleriens dans la sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.

LINKS

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamilton cycles in product graphs

F. Faase, Results from the counting program

F. Faase, Counting Hamilton cycles in product graphs

Index entries for sequences related to trees

P. Raff, Spanning Trees in Grid Graphs. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

P. Raff, Analysis of the Number of Spanning Trees of P_3 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

FORMULA

a(n) = 15a(n-1) - 32a(n-2) + 15a(n-3) - a(n-4), n>4.

G.f.: -x(x^2-1)/(x^4-15x^3+32x^2-15x+1) [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

a(n)=A001906(n)*A004254(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]

CROSSREFS

Sequence in context: A004344 A038339 A051545 this_sequence A015673 A125472 A098300

Adjacent sequences: A006235 A006236 A006237 this_sequence A006239 A006240 A006241

KEYWORD

nonn

AUTHOR

Frans Faase (Frans_LiXia(AT)wxs.nl)

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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