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A167072
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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}, {4, 5}}.
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1
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12, 6720, 3110400, 1423806720, 651286330860, 297900675072000, 136260356109480876, 62325740425973498880, 28507909150300692211200, 13039570449847302883368000, 5964323676112090939594326348, 2728092696767010687412666368000, 1247834652562251646622689145644236
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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}, {4, 5}}. Contains sequence, recurrence, generating function, and more.
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FORMULA
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a(n) = 525 a(n-1)
- 32415 a(n-2)
+ 696920 a(n-3)
- 5936265 a(n-4)
+ 19827675 a(n-5)
- 29313582 a(n-6)
+ 19827675 a(n-7)
- 5936265 a(n-8)
+ 696920 a(n-9)
- 32415 a(n-10)
+ 525 a(n-11)
- a(n-12).
G.f.: -12x (x^10 +35x^9 -2385x^8 +26040x^7 -54030x^6 +54030x^4 -26040x^3 +2385x^2 -35x-1) / (x^12 -525x^11 +32415x^10 -696920x^9 +5936265x^8 -19827675x^7 +29313582x^6 -19827675x^5 +5936265x^4 -696920x^3 +32415x^2 -525x+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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