A288037 Number of (undirected) paths in the n-web graph.

285, 984, 2855, 7488, 18431, 43504, 99783, 224280, 496727, 1087992, 2362607, 5095216, 10926255, 23318880, 49563959, 104972328, 221623847, 466594600, 979869471, 2053083648, 4292838335, 8958997584, 18664612775, 38822433208, 80631250551, 167235234264, 346415895503

Offset

3,1

Links

Colin Barker, Table of n, a(n) for n = 3..1000

Eric Weisstein's World of Mathematics, Graph Path

Eric Weisstein's World of Mathematics, Web Graph

Index entries for linear recurrences with constant coefficients, signature (8,-26,44,-41,20,-4).

Formula

a(n) = n*(-104+89*2^n-52*n-8*n^2)/4.

a(n) = 8*a(n-1)-26*a(n-2)+44*a(n-3)-41*a(n-4)+20*a(n-5)-4*a(n-6).

G.f.: x^3*(285 - 1296*x + 2393*x^2 - 2308*x^3 + 1146*x^4 - 232*x^5) / ((1 - x)^4*(1 - 2*x)^2). - Colin Barker, Jun 05 2017

Mathematica

Table[1/4 n (-104 + 89 2^n - 52 n - 8 n^2), {n, 3, 20}]
LinearRecurrence[{8, -26, 44, -41, 20, -4}, {285, 984, 2855, 7488, 18431, 43504}, 18]
CoefficientList[Series[(285 - 1296 x + 2393 x^2 - 2308 x^3 + 1146 x^4 - 232 x^5)/((1 - x)^4 (1 - 2 x)^2), {x, 0, 20}], x]

Prog

(PARI) Vec(x^3*(285 - 1296*x + 2393*x^2 - 2308*x^3 + 1146*x^4 - 232*x^5) / ((1 - x)^4*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Jun 05 2017

Crossrefs

Sequence in context: A339681 A249954 A043415 * A105921 A209311 A176712

Adjacent sequences: A288034 A288035 A288036 * A288038 A288039 A288040

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 04 2017

Status

approved