A102865 Base-4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, ... ).

1, 3, 9, 35, 137, 547, 2185, 8739, 34953, 139811, 559241, 2236963, 8947849, 35791395, 143165577, 572662307, 2290649225, 9162596899, 36650387593, 146601550371, 586406201481, 2345624805923, 9382499223689, 37529996894755, 150119987579017, 600479950316067

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

Formula

4^n = a(n) + A037576(n) for n >= 1.

a(n) + a(n+1) = A039301(n+2).

a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - Harvey P. Dale, Mar 23 2012

G.f.: 1 + x*(3-3*x-4*x^2)/((1-x)*(1+x)*(1-4*x)). - Colin Barker, Aug 28 2012

Mathematica

FromDigits[IntegerDigits[#], 4]&/@(NestList[FromDigits[Flatten[ IntegerDigits[#]/.{3->{2, 1}, 1->{0, 3}}]]&, 1, 30]) (* or *) LinearRecurrence[{4, 1, -4}, {1, 3, 9}, 31](* Harvey P. Dale, Mar 23 2012 *)

Crossrefs

Cf. A037576.

Sequence in context: A149017 A149018 A149019 * A046697 A151045 A369389

Adjacent sequences: A102862 A102863 A102864 * A102866 A102867 A102868

Keyword

base,easy,nonn

Author

Creighton Dement, Mar 01 2005

Extensions

More terms from Harvey P. Dale, Mar 23 2012

Status

approved