A244663 Binary representation of 4^n + 2^(n+1) - 1.

111, 10111, 1001111, 100011111, 10000111111, 1000001111111, 100000011111111, 10000000111111111, 1000000001111111111, 100000000011111111111, 10000000000111111111111, 1000000000001111111111111, 100000000000011111111111111, 10000000000000111111111111111

Offset: 1

Author

Colin Barker, Jul 08 2014

Keywords

• nonn
• easy
• base

Examples

			a(3) is 1001111 because A093069(3) = 79 which is 1001111 in base 2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..450
• Wikipedia, Kynea number
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A093069.

Programs

Magma

[-1/9 + 10^(1 + n)/9 + 100^n : n in [1..15]]; // Wesley Ivan Hurt, Jul 09 2014

Maple

A244663:=n->-1/9+10^(1+n)/9+100^n: seq(A244663(n), n=1..15); # Wesley Ivan Hurt, Jul 09 2014

Mathematica

Table[-1/9 + 10^(1 + n)/9 + 100^n, {n, 15}] (* Wesley Ivan Hurt, Jul 09 2014 *)
LinearRecurrence[{111,-1110,1000},{111,10111,1001111},20] (* Harvey P. Dale, Dec 11 2014 *)

PARI

vector(100, n, -1/9+10^(1+n)/9+100^n)

PARI

Vec(-x*(2000*x^2-2210*x+111)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100))

Formula

a(n) = -1/9+10^(1+n)/9+100^n.

a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3).

G.f.: -x*(2000*x^2-2210*x+111) / ((x-1)*(10*x-1)*(100*x-1)).