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A090843 Number of nodes on a tree with degree 11 interior nodes and degree 1 boundary nodes.

%I A090843 #26 May 07 2025 09:03:40
%S A090843 1,12,122,1222,12222,122222,1222222,12222222,122222222,1222222222,
%T A090843 12222222222,122222222222,1222222222222,12222222222222,
%U A090843 122222222222222,1222222222222222,12222222222222222,122222222222222222,1222222222222222222,12222222222222222222,122222222222222222222
%N A090843 Number of nodes on a tree with degree 11 interior nodes and degree 1 boundary nodes.
%C A090843 Sum of n-th row of triangle of powers of 10: 1; 1 10 1; 1 10 100 10 1; 1 10 100 1000 100 10 1; ... - _Philippe Deléham_, Feb 23 2014
%H A090843 Vincenzo Librandi, <a href="/A090843/b090843.txt">Table of n, a(n) for n = 0..100</a>
%H A090843 Li He, Xiangwei Liu, and Gilbert Strang, <a href="http://www-math.mit.edu/~gs/papers/mp.pdf">Trees with Cantor Eigenvalue Distribution</a>, Studies in Applied Mathematics, Vol. 110(2), 2003, pp. 123-138.
%H A090843 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A090843 a(n) = (11*10^n - 2)/9.
%F A090843 G.f.: (1+x)/((1-x)*(1-10*x)). - _Zerinvary Lajos_, Feb 25 2009
%F A090843 From _Philippe Deléham_, Feb 23 2014: (Start)
%F A090843 a(n) = 10*a(n-1) + 2, a(0) = 1.
%F A090843 a(n) = 11*a(n-1) - 10*a(n-2), a(0) = 1, a(1) = 12.
%F A090843 a(n) = Sum_{k=0..n} A112468(n,k)*11^k. (End)
%F A090843 E.g.f.: exp(x)*(11*exp(9*x) - 2)/9. - _Elmo R. Oliveira_, May 07 2025
%e A090843 a(0) = 1;
%e A090843 a(1) = 1 + 10 + 1 = 12;
%e A090843 a(2) = 1 + 10 + 100 + 10 + 1 = 122;
%e A090843 a(3) = 1 + 10 + 100 + 1000 + 100 + 10 + 1 = 1222; etc. - _Philippe Deléham_, Feb 23 2014
%p A090843 g:=(1+z)/((1-z)* (1-10*z)): gser:=series(g, z=0, 43): seq((coeff(gser, z, n)), n=0..24); # _Zerinvary Lajos_, Feb 25 2009
%t A090843 Table[(11 10^n - 2)/9, {n, 0, 20}] (* _Vincenzo Librandi_, Feb 24 2014 *)
%Y A090843 Cf. A112468, A112739.
%K A090843 easy,nonn
%O A090843 0,2
%A A090843 _Paul Barry_, Dec 09 2003