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A347725
Number of irredundant sets in the (2n-1)-triangular snake graph (for n > 1).
0
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
Eric Weisstein's World of Mathematics, Irredundant Set
Eric Weisstein's World of Mathematics, Triangular Snake Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 11 2021
STATUS
approved