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A349416
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a(n) is the Wiener index of a broom on 2n vertices of which n+2 are pendant.
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2
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25, 54, 100, 167, 259, 380, 534, 725, 957, 1234, 1560, 1939, 2375, 2872, 3434, 4065, 4769, 5550, 6412, 7359, 8395, 9524, 10750, 12077, 13509, 15050, 16704, 18475, 20367, 22384, 24530, 26809, 29225, 31782, 34484, 37335, 40339, 43500, 46822, 50309, 53965, 57794, 61800, 65987
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OFFSET
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3,1
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COMMENTS
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A broom on 2n vertices is a caterpillar that is obtained by adding n pendant vertices to the first (or last) internal vertex of a path on n >= 3 vertices.
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LINKS
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FORMULA
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a(n) = 2n^3/3 + n^2/2 + 5n/6.
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EXAMPLE
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For n=3 the value a(3)=25 gives the Wiener index of a star graph on 6 vertices. For n=4, a(4)=54 gives the Wiener index of a broom graph on 8 vertices (6 of which are leaves).
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MATHEMATICA
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nterms=50; Table[2n^3/3+n^2/2+5n/6, {n, 3, nterms+2}] (* Paolo Xausa, Nov 22 2021 *)
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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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