A108020 a(n) is the number whose binary representation is the concatenation of n strings of the four digits "1100".

0, 12, 204, 3276, 52428, 838860, 13421772, 214748364, 3435973836, 54975581388, 879609302220, 14073748835532, 225179981368524, 3602879701896396, 57646075230342348, 922337203685477580, 14757395258967641292, 236118324143482260684, 3777893186295716170956

Offset: 0

Author

Alexandre Wajnberg, May 31 2005

Keywords

• easy
• nonn

Comments

Numbers whose base-16 representation consists entirely of 12's; 12 times base-16 repunits. - Franklin T. Adams-Watters, Mar 29 2006

Examples

			a(3) = 3276 because 3276 written in base 2 is the digit string "1100" written three times: 110011001100.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..800
• Index entries for linear recurrences with constant coefficients, signature (17,-16).

Crossrefs

Cf. A131865, A182512.

Programs

Mathematica

Table[ FromDigits[ Flatten[ Table[{1, 1, 0, 0}, {i, n}]], 2], {n, 0, 16}] (* Robert G. Wilson v, Jun 01 2005 *)
Table[FromDigits[PadRight[{},4n,{1,1,0,0}],2],{n,0,20}] (* Harvey P. Dale, Aug 12 2012 *)

PARI

concat(0, Vec(12*x/((1-x)*(1-16*x)) + O(x^100))) \\ Colin Barker, Dec 06 2015

PARI

a(n)=12*(16^n - 1)/15 \\ Charles R Greathouse IV, Nov 01 2022

Formula

a(n) = 12*(16^n - 1)/15. - Franklin T. Adams-Watters, Mar 29 2006

From Colin Barker, Dec 06 2015: (Start)

a(n) = 17*a(n-1) - 16*a(n-2) for n > 1.

G.f.: 12*x / ((1-x)*(1-16*x)).

(End)

a(n) = 4*A182512(n). - Jamie Simpson, Oct 25 2022

a(n) = 12*A131865(n-1) for n>0. - Hugo Pfoertner, Nov 01 2022

Extensions

More terms from Robert G. Wilson v, Jun 01 2005