A347725 Number of irredundant sets in the (2n-1)-triangular snake graph (for n > 1).

1, 4, 10, 25, 64, 163, 415, 1057, 2692, 6856, 17461, 44470, 113257, 288445, 734617, 1870936, 4764934, 12135421, 30906712, 78713779, 200469691, 510559873, 1300303216, 3311635996, 8434135081, 21480209374, 54706189825, 139326724105, 354839847409, 903712608748

Offset

1,2

Comments

The 1-triangular snake is K_1, which has two trivial irredundant sets ({} and {1}), which differs from a(1).

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Irredundant Set

Eric Weisstein's World of Mathematics, Triangular Snake Graph

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

Formula

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

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

Mathematica

Table[-RootSum[-1 - # - 2 #^2 + #^3 &, -9 #^n - 16 #^(n + 1) + 5 #^(n + 2) &]/29, {n, 20}]
LinearRecurrence[{2, 1, 1}, {1, 4, 10}, 20]
CoefficientList[Series[(-1 - 2 x - x^2)/(-1 + 2 x + x^2 + x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A225301 A298412 A289245 * A097136 A049348 A282389

Adjacent sequences: A347722 A347723 A347724 * A347726 A347727 A347728

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 11 2021

Status

approved