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A006235
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Complexity of doubled cycle (regarding case n = 2 as a multigraph).
(Formerly M4849)
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5
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1, 12, 75, 384, 1805, 8100, 35287, 150528, 632025, 2620860, 10759331, 43804800, 177105253, 711809364, 2846259375, 11330543616, 44929049777, 177540878700, 699402223099, 2747583822720, 10766828545725, 42095796462852, 164244726238343
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| In plain English, a(n) is the number of spanning trees of the n-prism graph Y_n. - Eric Weisstein, Jul 15 2011
Also the number of spanning trees of the n-web graph. - Eric Weisstein, Jul 15 2011
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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
| 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.
Eric Weisstein's World of Mathematics, Prism Graph
Eric Weisstein's World of Mathematics, Spanning Tree
Eric Weisstein's World of Mathematics, Web Graph
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FORMULA
| G.f.: x(1+2x-10x^2+2x^3+x^4)/((1-x)*(1-4x+x^2))^2.
a(n)=10a(n-1)-35a(n-2)+52a(n-3)-35a(n-4)+10a(n-5)-a(n-6), n>5.
a(n)=(n/2)*A129743(n) [From Woong Kook and Seung Kyoon Shin (andrewk(AT)math.uri.edu), Jan 13 2009]
a(n) = 1/2*(-2 + (2 - sqrt(3))^n + (2 + Sqrt(3))^n)*n [From Eric Weisstein, Jul 15 2011]
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MAPLE
| A006235:=(1+2*z-10*z**2+2*z**3+z**4)/(z-1)**2/(z**2-4*z+1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| LinearRecurrence[{10, -35, 52, -35, 10, -1}, {0, 1, 12, 75, 384, 1805}, 20]
Table[1/2 (-2 + (2 - Sqrt[3])^n + (2 + Sqrt[3])^n) n, {n, 0, 20}] // Expand
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PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x-10*x^2+2*x^3+x^4)/((1-x)*(1-4*x+x^2))^2+x*O(x^n), n))
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CROSSREFS
| Cf. A006237. Apart from a(2) coincides with A072373.
Sequence in context: A003368 A092867 A053310 * A009642 A051104 A044199
Adjacent sequences: A006232 A006233 A006234 * A006236 A006237 A006238
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Michael Somos, Jul 19 2002
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