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A167071
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Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}}.
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1
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4, 1376, 361860, 92544256, 23575404820, 6002044445280, 1527898117755412, 388939442019315712, 99007542753465378420, 25203122804459545322080, 6415645979596681028789108, 1633151297922105531036929280, 415731036835959295502046104100, 105827485262836457484100780941664
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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}, {2, 5}, {3, 5}}. Contains sequence, recurrence, generating function, and more.
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FORMULA
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a(n) = 344 a(n-1)
- 25540 a(n-2)
+ 745448 a(n-3)
- 10445708 a(n-4)
+ 76194968 a(n-5)
- 303860988 a(n-6)
+ 687124520 a(n-7)
- 899525622 a(n-8)
+ 687124520 a(n-9)
- 303860988 a(n-10)
+ 76194968 a(n-11)
- 10445708 a(n-12)
+ 745448 a(n-13)
- 25540 a(n-14)
+ 344 a(n-15)
- a(n-16)
G.f.: -4x (x^14 -2331x^12 +56416x^11 -467115x^10 +1546624x^9 -1949983x^8 +1949983x^6 -1546624x^5 +467115x^4 -56416x^3 +2331x^2 -1)/ (x^16 -344x^15 +25540x^14 -745448x^13 +10445708x^12 -76194968x^11 +303860988x^10 -687124520x^9 +899525622x^8 -687124520x^7 +303860988x^6 -76194968x^5 +10445708x^4 -745448x^3 +25540x^2 -344x+1).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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