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A033082 Numbers n with property that all pairs of consecutive base 4 digits differ by 2. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)