A376478 a(1) = 1, a(2) = 2, and a(n) = 3^(n-2) for n > 2.

1, 2, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987, 22876792454961

Offset: 1

Author

Stefano Spezia, Sep 24 2024

Keywords

• nonn
• easy

Comments

Graham's conjecture: also numbers k such sigma(k) - k = floor(k/2). See Guy.

Also the domination number of the n-Sierpinski gasket graph. - Eric W. Weisstein, Mar 10 2025

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B2.

Links

• Eric Weisstein's World of Mathematics, Domination Number.
• Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph.
• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A000244, A140429, A001065, A004526.

Programs

Mathematica

LinearRecurrence[{3},{1,2,3},30]

Python

def A376478(n): return n if n<3 else 3**(n-2) # Chai Wah Wu, Nov 13 2024

Formula

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

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

E.g.f.: (2 + exp(3*x) + 3*x)/3.