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

Author

Creighton Dement, Mar 01 2005

Keywords

• base
• easy
• nonn

Links

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

Crossrefs

Cf. A037576.

Programs

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 *)

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

Extensions

More terms from Harvey P. Dale, Mar 23 2012