%I #19 Sep 10 2024 11:03:51

%S 1,0,3,18,69,228,711,2166,6537,19656,59019,177114,531405,1594284,

%T 4782927,14348862,43046673,129140112,387420435,1162261410,3486784341,

%U 10460353140,31381059543,94143178758,282429536409,847288609368,2541865828251,7625597484906,22876792454877

%N a(n) = 3^n - 3*n.

%C 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.

%H Vincenzo Librandi, <a href="/A107583/b107583.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).

%F From _Elmo R. Oliveira_, Sep 09 2024: (Start)

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

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

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

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

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

%o (Magma) [3^n-3*n: n in [0..30]]; // _Vincenzo Librandi_, Oct 22 2011

%o (PARI) a(n)=3^n-3*n \\ _Charles R Greathouse IV_, Sep 08 2012

%Y Cf. A107584, A107585.

%K nonn,easy

%O 0,3

%A _Zak Seidov_, May 16 2005

%E Corrected by _Charles R Greathouse IV_, Sep 08 2012