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

0,2

Comments

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

Links

Colin Barker, Table of n, a(n) for n = 0..800

Index entries for linear recurrences with constant coefficients, signature (17,-16).

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

From Elmo R. Oliveira, Sep 18 2025: (Start)

E.g.f.: 4*exp(x)*(exp(15*x) - 1)/5.

a(n) = 3*A141032(n). (End)

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A131865, A141032, A182512.

Sequence in context: A083932 A080316 A357568 * A097193 A051688 A198529

Adjacent sequences: A108017 A108018 A108019 * A108021 A108022 A108023

Keyword

easy,nonn

Author

Alexandre Wajnberg, May 31 2005

Extensions

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

Status

approved