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Search: id:A027836
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| A027836 |
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Total number of vertices in loopless rooted planar maps (with n-1 edges). |
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4
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| 1, 2, 8, 43, 268, 1824, 13156, 98865, 765948, 6075256, 49094708, 402801425, 3346590068, 28099903160, 238079915640, 2032914717645, 17476713955548, 151143219598008, 1314045772469632, 11478299163026540, 100688538612524720
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The number of rooted isthmusless n-edge maps in the plane (planar with a distinguished outside face). - Valery A. Liskovets (liskov(AT)im.bas-net.by), Mar 17 2005
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REFERENCES
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L. M. Koganov, V. A. Liskovets, T. R. S. Walsh, Total vertex enumeration in rooted planar maps, Ars Combin. 54 (2000), 149-160.
V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
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LINKS
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V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.
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FORMULA
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12*n*(4*n-1)!*(5*n^2+13*n+2)/(n!*(3*n+3)!).
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MAPLE
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12*n*(4*n-1)!*(5*n^2+13*n+2)/(n!*(3*n+3)!);
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CROSSREFS
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Cf. A000260, A005470, A002293.
Adjacent sequences: A027833 A027834 A027835 this_sequence A027837 A027838 A027839
Sequence in context: A012917 A050637 A020023 this_sequence A007169 A106327 A009309
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KEYWORD
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nonn
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AUTHOR
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Valery Liskovets (liskov(AT)NALW01.math.tu-dresden.de)
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