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
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 11 2021
STATUS
approved