A037726 Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,3,1.

2, 14, 101, 708, 4958, 34706, 242945, 1700616, 11904314, 83330198, 583311389, 4083179724, 28582258070, 200075806490, 1400530645433, 9803714518032, 68626001626226, 480382011383582, 3362674079685077, 23538718557795540, 164771029904568782, 1153397209331981474

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,0,0,1,-7).

Formula

a(n) = 7*a(n-1) + a(n-4) - 7*a(n-5).

From Colin Barker, Dec 24 2015: (Start)

a(n) = 1/200*(-25*(-1)^n+(8+6*i)*(-i)^n+(8-6*i)*i^n+59*7^n-50) where i=sqrt(-1).

G.f.: x*(2+3*x^2+x^3) / ((1-x)*(1+x)*(1-7*x)*(1+x^2)).

(End)

Mathematica

Table[FromDigits[PadRight[{}, n, {2, 0, 3, 1}], 7], {n, 30}] (* or *) LinearRecurrence[{7, 0, 0, 1, -7}, {2, 14, 101, 708, 4958}, 30] (* Harvey P. Dale, Sep 01 2016 *)

Prog

(PARI) Vec(x*(2+3*x^2+x^3)/((1-x)*(1+x)*(1-7*x)*(1+x^2)) + O(x^30)) \\ Colin Barker, Dec 24 2015

Crossrefs

Sequence in context: A074620 A185010 A144277 * A037621 A085372 A123525

Adjacent sequences: A037723 A037724 A037725 * A037727 A037728 A037729

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved