A033082 Numbers in which all pairs of consecutive base-4 digits differ by 2.

1, 2, 3, 7, 8, 13, 29, 34, 55, 119, 136, 221, 477, 546, 887, 1911, 2184, 3549, 7645, 8738, 14199, 30583, 34952, 56797, 122333, 139810, 227191, 489335, 559240, 908765, 1957341, 2236962, 3635063, 7829367, 8947848, 14540253, 31317469, 35791394, 58161015

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,1,0,0,-4).

Formula

G.f.: x*(x^5+3*x^3+3*x^2+2*x+1) / (4*x^9-x^6-4*x^3+1). - Colin Barker, May 31 2015

a(n) = 4*a(n-3) + a(n-6) - 4*a(n-9) for n > 9. - Colin Barker, Jun 01 2015

Maple

a:= proc(n) option remember; `if`(n<1, 0,
      a(n-3)*4 +[1, 2, 3, 3, 0, 1][1+irem(n-1, 6)])
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 31 2015

Mathematica

Join[{1, 2, 3}, Select[Range[230000], Union[Abs[Differences[ IntegerDigits[ #, 4]]]]=={2}&]] (* Harvey P. Dale, Sep 20 2011 *)

Prog

(PARI) Vec(x*(x^5+3*x^3+3*x^2+2*x+1)/(4*x^9-x^6-4*x^3+1) + O(x^100)) \\ Colin Barker, Jun 01 2015

Crossrefs

Cf. A033077.

Sequence in context: A003307 A105601 A199971 * A084406 A075648 A071527

Adjacent sequences: A033079 A033080 A033081 * A033083 A033084 A033085

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved