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A102865 Base 4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, ... ). 0
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 (list; graph; refs; listen; history; text; internal format)
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+1) = a(n+1) + A037576(n+1)_1 = (1/2)(a(n+2) - a(n)); a(n) + a(n+1) = A039301(n+2).

a(0)=1, a(1)=3, a(2)=9, a(n)=4*a(n-1)+a(n-2)-4*a(n-3). [From 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 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 1tesforseq[ + j' - k' + 'ii' - 'ij' - 'ik' ], 1vesforseq(n) = 4^n, 1lesforseq = A037576, apart from initial term. ForType 1A.

CROSSREFS

Cf. A037576.

Sequence in context: A149017 A149018 A149019 * A046697 A151045 A225041

Adjacent sequences:  A102862 A102863 A102864 * A102866 A102867 A102868

KEYWORD

base,easy,nonn,uned

AUTHOR

Creighton Dement, Mar 01 2005

EXTENSIONS

More terms from Harvey P. Dale, Mar 23 2012

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.