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A033082
Numbers in which 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
OFFSET
1,2
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
KEYWORD
nonn,base,easy
STATUS
approved