A307685 Clique covering number of the n-Sierpinski gasket graph.

1, 3, 6, 17, 48, 143, 426, 1277, 3828, 11483, 34446, 103337, 310008, 930023, 2790066, 8370197, 25110588, 75331763, 225995286, 677985857, 2033957568, 6101872703, 18305618106, 54916854317, 164750562948, 494251688843, 1482755066526, 4448265199577, 13344795598728, 40034386796183

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Clique Covering Number.

Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.

Index entries for linear recurrences with constant coefficients, signature (3,1,-3).

Formula

a(n) = (7*3^(n-2) + (-1)^n + 4)/4 for n > 1. - Andrew Howroyd, May 30 2025

From Elmo R. Oliveira, Apr 10 2026: (Start)

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

G.f.: x*(1 - 4*x^2 - x^3)/((1 + x)*(1 - x)*(1 - 3*x)).

E.g.f.: (1/36)*(9*exp(-x) + 36*exp(x) + 7*exp(3*x) - 4*(13 + 3*x)). (End)

Mathematica

LinearRecurrence[{3, 1, -3}, {1, 3, 6, 17}, 30] (* Paolo Xausa, Apr 16 2026 *)

Prog

(PARI) a(n) = if(n==1, 1, (7*3^(n-2) + (-1)^n + 4)/4) \\ Andrew Howroyd, May 30 2025

Crossrefs

Cf. A307702.

Sequence in context: A099511 A389124 A204517 * A360273 A287901 A354878

Adjacent sequences: A307682 A307683 A307684 * A307686 A307687 A307688

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 21 2019

Extensions

a(9) onwards from Andrew Howroyd, May 30 2025

Status

approved