A287426 Number of connected induced subgraphs in the n-sun graph.

3, 14, 47, 164, 577, 2046, 7275, 25896, 92213, 328402, 1169599, 4165564, 14835849, 52838630, 188187539, 670239824, 2387094493, 8501763066, 30279478119, 107841960420, 384084837425, 1367938433038, 4871984973883, 17351831787640, 61799465310597, 220102059506978

Offset: 1

Author

Eric W. Weisstein, May 24 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Sun Graph
• Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
• Index entries for linear recurrences with constant coefficients, signature (5,-5,-1,2).

Crossrefs

Cf. A206776.

Programs

Mathematica

LinearRecurrence[{5, -5, -1, 2}, {3, 14, 47, 164}, 20]

PARI

Vec(x*(3 - x - 8*x^2 + 2*x^3) / ((1 - x)^2*(1 - 3*x - 2*x^2)) + O(x^40)) \\ Colin Barker, May 25 2017

Formula

a(n) = A206776(n) + n - 1.

From Colin Barker, May 25 2017: (Start)

G.f.: x*(3 - x - 8*x^2 + 2*x^3)/((1 - x)^2*(1 - 3*x - 2*x^2)).

a(n) = -1 + n + ((3-sqrt(17))/2)^n + ((3+sqrt(17))/2)^n.

a(n) = 5*a(n-1) - 5*a(n-2) - a(n-3) + 2*a(n-4) for n>4. (End)