A138894 Expansion of (1+x)/(1-10*x+9*x^2).

1, 11, 101, 911, 8201, 73811, 664301, 5978711, 53808401, 484275611, 4358480501, 39226324511, 353036920601, 3177332285411, 28595990568701, 257363915118311, 2316275236064801, 20846477124583211, 187618294121248901

Offset: 0

Author

Paul Barry, Apr 02 2008

Keywords

• easy
• nonn

Comments

Orbit starting at 1 of A138893: a(n)=A138893^(n)(1). Partial sums of A003952.

Sum of n-th row of triangle of powers of 9: 1; 1 9 1; 1 9 81 9 1; 1 9 81 729 81 9 1; ... - Philippe Deléham, Feb 22 2014

Examples

			a(0) = 1;
a(1) = 1 + 9 + 1 = 11;
a(2) = 1 + 9 + 81 + 9 + 1 = 101;
a(3) = 1 + 9 + 81 + 729 + 81 + 9 + 1 = 911; etc. - _Philippe Deléham_, Feb 22 2014
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (10,-9).

Crossrefs

Cf. A096053 ((3*9^n-1)/2), a(n+1)=9a(n)-4 in A135423.

Cf. A002452, A003952, A135522, A138893.

Programs

Magma

[(5/4)*9^n-1/4: n in [0..20]]; // Vincenzo Librandi, Aug 09 2011

Mathematica

Table[(5*9^n - 1)/4, {n, 0, 18}] (* L. Edson Jeffery, Feb 13 2015 *)

PARI

Vec((1+x)/(1-10*x+9*x^2) + O(x^30)) \\ Michel Marcus, Feb 13 2015

Formula

G.f.: (1+x)/((1-x)*(1-9x)).

a(n) = (5/4)*9^n - 1/4.

a(n) = A002452(n) + A002452(n+1).

Bisection of A135522/3. a(n+1)=9*a(n)+2. - Paul Curtz, Apr 22 2008

a(n) = Sum_{k=0..n} A112468(n,k)*10^k. - Philippe Deléham, Feb 22 2014