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A167063
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Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 5}}.
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1
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21, 16905, 11515392, 7766579625, 5234202655605, 3527304596766720, 2377020102892371573, 1601852459790100499625, 1079473906452564386072064, 727447713589013080159967625, 490220442215546503112745464469, 330355127203424593855513657344000, 222623335689469074506271256084716693
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OFFSET
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1,1
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs a X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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P. Raff, Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 5}}. Contains sequence, recurrence, generating function, and more.
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FORMULA
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a(n) = 805 a(n-1)
- 94300 a(n-2)
+ 4128845 a(n-3)
- 82955561 a(n-4)
+ 801676960 a(n-5)
- 3659544950 a(n-6)
+ 8726681390 a(n-7)
- 11584112776 a(n-8)
+ 8726681390 a(n-9)
- 3659544950 a(n-10)
+ 801676960 a(n-11)
- 82955561 a(n-12)
+ 4128845 a(n-13)
- 94300 a(n-14)
+ 805 a(n-15)
- a(n-16)
G.f.: -21x(x^14 -5373x^12 +196420x^11 -2311184x^10 +8452500x^9 -10863790x^8 +10863790x^6 -8452500x^5 +2311184x^4 -196420x^3 +5373x^2 -1)/ (x^16 -805x^15 +94300x^14 -4128845x^13 +82955561x^12 -801676960x^11 +3659544950x^10 -8726681390x^9 +11584112776x^8 -8726681390x^7 +3659544950x^6 -801676960x^5 +82955561x^4 -4128845x^3 +94300x^2 -805x +1).
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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