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A291919
Number of (undirected) paths in the n-wheel graph.
0
0, 1, 9, 30, 78, 175, 351, 644, 1100, 1773, 2725, 4026, 5754, 7995, 10843, 14400, 18776, 24089, 30465, 38038, 46950, 57351, 69399, 83260, 99108, 117125, 137501, 160434, 186130, 214803, 246675, 281976, 320944, 363825, 410873, 462350, 518526, 579679, 646095, 718068
OFFSET
1,3
COMMENTS
Extended to a(1)-a(3) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Graph Path
Eric Weisstein's World of Mathematics, Wheel Graph
FORMULA
a(n) = (n - 1)*(2*n^3 - 12*n^2 + 43*n - 48)/6.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x^2*(1 + 4*x - 5*x^2 + 8*x^3)/(1 - x)^5.
MATHEMATICA
Table[(n - 1) (2 n^3 - 12 n^2 + 43 n - 48)/6, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 9, 30, 78}, 20]
CoefficientList[Series[x (1 + 4 x - 5 x^2 + 8 x^3)/(1 - x)^5, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A273604 A273640 A344522 * A301988 A334853 A212517
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 07 2017
STATUS
approved