A386707 a(n) = Lucas(n) + 6.

7, 9, 10, 13, 17, 24, 35, 53, 82, 129, 205, 328, 527, 849, 1370, 2213, 3577, 5784, 9355, 15133, 24482, 39609, 64085, 103688, 167767, 271449, 439210, 710653, 1149857, 1860504, 3010355, 4870853, 7881202, 12752049, 20633245, 33385288, 54018527, 87403809

Offset

1,1

Comments

For n >= 4, also the number of independent vertex sets in the (n-3)-Plummer-Toft graph.

Links

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Independent Vertex Set.

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

a(n) = A000032(n) + 6.

a(n) = 2*a(n-1)-a(n-3).

G.f.: -(x*(-7+5*x+8*x^2))/((-1+x)*(-1+x+x^2)).

Mathematica

Table[LucasL[n] + 6, {n, 20}]
LucasL[Range[20]] + 6
LinearRecurrence[{2, 0, -1}, {7, 9, 10}, 20]
CoefficientList[Series[-(-7 + 5 x + 8 x^2)/((-1 + x) (-1 + x + x^2)), {x, 0, 20}], x]

Crossrefs

Cf. A000032 (Lucas numbers).

Sequence in context: A151913 A095034 A138579 * A118621 A117933 A381040

Adjacent sequences: A386704 A386705 A386706 * A386708 A386709 A386710

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 03 2025

Status

approved