A094620 Expansion of x*(11 + 22*x + 20*x^2)/((1-x)*(1+x)*(1 - 10*x^2)).

0, 11, 22, 141, 242, 1441, 2442, 14441, 24442, 144441, 244442, 1444441, 2444442, 14444441, 24444442, 144444441, 244444442, 1444444441, 2444444442, 14444444441, 24444444442, 144444444441, 244444444442, 1444444444441, 2444444444442, 14444444444441

Offset

0,2

Comments

Previous name: "A palindromic sequence whose n-th term digits sum to 2n. (See Formula for definition.)"

a(0) = 0; for n > 0, a(n) is the k-digit number having 1 (for odd n) or 2 (for even n) as its first and last digits, and 4 for each of the remaining k-2 digits, where k = floor((n+3)/2).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Formula

a(n) = 10^(n/2)*(11/9 + 13*sqrt(10)/18 + (11/9 - 13*sqrt(10)/18)*(-1)^n) + (-1)^n/2 - 53/18.

a(n) = (A094621(n) + A094622(n))/2.

From Colin Barker, Nov 19 2016: (Start)

a(n) = 11*a(n-2) - 10*a(n-4) for n > 3.

G.f.: x*(11 + 22*x + 20*x^2) / ((1 - x)*(1 + x)*(1 - 10*x^2)).

(End)

Mathematica

LinearRecurrence[{0, 11, 0, -10}, {0, 11, 22, 141}, 50] (* G. C. Greubel, Nov 20 2016 *)

Prog

(PARI) concat(0, Vec(x*(11 + 22*x + 20*x^2) / ((1 - x)*(1 + x)*(1 - 10*x^2)) + O(x^30))) \\ Colin Barker, Nov 19 2016

Crossrefs

Sequence in context: A061852 A083511 A067894 * A077431 A118133 A345404

Adjacent sequences: A094617 A094618 A094619 * A094621 A094622 A094623

Keyword

easy,nonn,base

Author

Paul Barry, May 15 2004

Status

approved