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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

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OFFSET

0,2

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (10,-9).

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

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

CROSSREFS

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

Cf. A002452, A003952, A135522, A138893.

Sequence in context: A125399 A163146 A037550 * A287832 A122105 A332853

Adjacent sequences: A138891 A138892 A138893 * A138895 A138896 A138897

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 02 2008

STATUS

approved