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

1, 12, 122, 1222, 12222, 122222, 1222222, 12222222, 122222222, 1222222222, 12222222222, 122222222222, 1222222222222, 12222222222222, 122222222222222, 1222222222222222, 12222222222222222, 122222222222222222, 1222222222222222222, 12222222222222222222, 122222222222222222222

Offset: 0

Author

Paul Barry, Dec 09 2003

Keywords

• easy
• nonn

Comments

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

Examples

			a(0) = 1;
a(1) = 1 + 10 + 1 = 12;
a(2) = 1 + 10 + 100 + 10 + 1 = 122;
a(3) = 1 + 10 + 100 + 1000 + 100 + 10 + 1 = 1222; etc. - _Philippe Deléham_, Feb 23 2014
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Li He, Xiangwei Liu, and Gilbert Strang, Trees with Cantor Eigenvalue Distribution, Studies in Applied Mathematics, Vol. 110(2), 2003, pp. 123-138.
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A112468, A112739.

Programs

Maple

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

Mathematica

Table[(11 10^n - 2)/9, {n, 0, 20}] (* Vincenzo Librandi, Feb 24 2014 *)

Formula

a(n) = (11*10^n - 2)/9.

G.f.: (1+x)/((1-x)*(1-10*x)). - Zerinvary Lajos, Feb 25 2009

From Philippe Deléham, Feb 23 2014: (Start)

a(n) = 10*a(n-1) + 2, a(0) = 1.

a(n) = 11*a(n-1) - 10*a(n-2), a(0) = 1, a(1) = 12.

a(n) = Sum_{k=0..n} A112468(n,k)*11^k. (End)

E.g.f.: exp(x)*(11*exp(9*x) - 2)/9. - Elmo R. Oliveira, May 07 2025