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

1,1

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A206776.

Sequence in context: A104196 A281869 A202144 * A246149 A201349 A006900

Adjacent sequences: A287423 A287424 A287425 * A287427 A287428 A287429

Keyword

nonn,easy

Author

Eric W. Weisstein, May 24 2017

Status

approved