A037610 Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2,3.

1, 12, 123, 1231, 12312, 123123, 1231231, 12312312, 123123123, 1231231231, 12312312312, 123123123123, 1231231231231, 12312312312312, 123123123123123, 1231231231231231, 12312312312312312, 123123123123123123, 1231231231231231231, 12312312312312312312

Offset

1,2

Comments

Periodic sequences of this type can be easily calculated by a(n) = floor(q*10^n/(10^m-1)), where q is the number representing the periodic digit pattern (=123 for this sequence) and m is the period length. - Hieronymus Fischer Jan 03 2013

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (10,0,1,-10).

Formula

a(n) = floor((41/333)*10^n). - Hieronymus Fischer, Jan 03 2013

From Colin Barker, Apr 30 2014: (Start)

a(n) = 10*a(n-1) + a(n-3) - 10*a(n-4).

G.f.: x*(3*x^2 + 2*x + 1) / ((x - 1)*(10*x - 1)*(x^2 + x + 1)). (End)

a(n) = (41*10^n - 27*n - 50 + 90*floor(n/3) - 9*floor((n - 1)/3))/333. - Bruno Berselli, Sep 13 2018

Maple

A037610:=n->floor((41/333)*10^n); seq(A037610(n), n=1..20); # Wesley Ivan Hurt, Apr 19 2014

Mathematica

a[n_] := Floor[41/333*10^n]; Array[a, 19] (* Robert G. Wilson v, Apr 18 2014 *)
Table[FromDigits[PadRight[{}, n, {1, 2, 3}]], {n, 20}] (* or *) LinearRecurrence[ {10, 0, 1, -10}, {1, 12, 123, 1231}, 20] (* Harvey P. Dale, May 09 2014 *)

Prog

(PARI) A037610(n)=10^n*41\333  \\ M. F. Hasler, Jan 13 2013
(PARI) Vec(x*(3*x^2+2*x+1)/((x-1)*(10*x-1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 30 2014
(Magma) [(41*10^n-27*n-50+90*Floor(n/3)-9*Floor((n-1)/3))/333: n in [1..30]]; // Bruno Berselli, Sep 13 2018

Crossrefs

Sequence in context: A144165 A113572 A037701 * A035239 A344183 A057137

Adjacent sequences: A037607 A037608 A037609 * A037611 A037612 A037613

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved