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A006417
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Number of loopless rooted planar maps with 4 faces and n vertices and no isthmuses.
(Formerly M5091)
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2
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1, 20, 131, 469, 1262, 2862, 5780, 10725, 18647, 30784, 48713, 74405, 110284, 159290, 224946, 311429, 423645, 567308, 749023, 976373, 1258010, 1603750, 2024672, 2533221, 3143315, 3870456, 4731845, 5746501, 6935384, 8321522, 9930142, 11788805, 13927545, 16379012
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OFFSET
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2,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (2160+846*n-1027*n^2-345*n^3+125*n^4+39*n^5+2*n^6)/360.
G.f.: -x^2*(5*x^6-29*x^5+65*x^4-63*x^3+12*x^2+13*x+1) / (x-1)^7. (End)
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PROG
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(PARI) a(n)={if(n<2, 0, (2*n^6 + 39*n^5 + 125*n^4 - 345*n^3 - 1027*n^2 + 846*n + 2160)/360)} \\ Andrew Howroyd, Apr 01 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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