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A093135 Expansion of g.f. (1-8*x)/((1-x)*(1-10*x)).

%I A093135 #26 Apr 03 2025 14:11:37
%S A093135 1,3,23,223,2223,22223,222223,2222223,22222223,222222223,2222222223,
%T A093135 22222222223,222222222223,2222222222223,22222222222223,
%U A093135 222222222222223,2222222222222223,22222222222222223,222222222222222223,2222222222222222223,22222222222222222223,222222222222222222223
%N A093135 Expansion of g.f. (1-8*x)/((1-x)*(1-10*x)).
%C A093135 Second binomial transform of 2*A001045(3*n)/3 + (-1)^n.
%C A093135 Partial sums of A093136.
%C A093135 A convex combination of 10^n and 1.
%C A093135 In general the second binomial transform of k*Jacobsthal(3*n)/3 + (-1)^n is 1, 1+k, 1+11*k, 1+111*k, ... This is the case for k=2.
%C A093135 Essentially the same as A091628 (cf. 2nd formula). - _Georg Fischer_, Oct 06 2018
%C A093135 a(n) is 3^n represented in bijective base-3 numeration. - _Alois P. Heinz_, Aug 26 2019
%H A093135 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>.
%H A093135 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A093135 a(n) = (2*10^n + 7)/9.
%F A093135 a(n) = 10*a(n-1) - 7 (with a(0)=1). - _Vincenzo Librandi_, Aug 02 2010
%F A093135 From _Elmo R. Oliveira_, Apr 03 2025: (Start)
%F A093135 E.g.f.: exp(x)*(7 + 2*exp(9*x))/9.
%F A093135 a(n) = 11*a(n-1) - 10*a(n-2).
%F A093135 a(n) = (A062397(n) - A002279(n))/2. (End)
%Y A093135 Cf. A001045, A002279, A047855, A062397, A091628, A093136.
%K A093135 nonn,easy
%O A093135 0,2
%A A093135 _Paul Barry_, Mar 24 2004
%E A093135 More terms from _Elmo R. Oliveira_, Apr 03 2025