A291919 Number of (undirected) paths in the n-wheel graph.

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

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Graph Path

Eric Weisstein's World of Mathematics, Wheel Graph

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Adjacent sequences: A291916 A291917 A291918 * A291920 A291921 A291922

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 07 2017

Status

approved