A107583 a(n) = 3^n - 3*n.

1, 0, 3, 18, 69, 228, 711, 2166, 6537, 19656, 59019, 177114, 531405, 1594284, 4782927, 14348862, 43046673, 129140112, 387420435, 1162261410, 3486784341, 10460353140, 31381059543, 94143178758, 282429536409, 847288609368, 2541865828251, 7625597484906, 22876792454877

Offset: 0

Author

Zak Seidov, May 16 2005

Keywords

• nonn
• easy

Comments

a(n) is the number k such that the number m with n 3's and k 1's has digit product = digit sum = 3^n.

Examples

			Corresponding numbers m are 1, 3, 11133, 111111111111111111333, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A107584, A107585.

Programs

Magma

[3^n-3*n: n in [0..30]]; // Vincenzo Librandi, Oct 22 2011

Mathematica

Table[3^m-3*m, {m, 0, 20}]

PARI

a(n)=3^n-3*n \\ Charles R Greathouse IV, Sep 08 2012

Formula

From Elmo R. Oliveira, Sep 09 2024: (Start)

G.f.: (1 - 5*x + 10*x^2)/((1 - 3*x)*(1 - x)^2).

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

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3) for n > 2. (End)

Extensions

Corrected by Charles R Greathouse IV, Sep 08 2012