A033125 Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.

1, 7, 50, 351, 2457, 17200, 120401, 842807, 5899650, 41297551, 289082857, 2023580000, 14165060001, 99155420007, 694087940050, 4858615580351, 34010309062457, 238072163437200, 1666505144060401, 11665536008422807, 81658752058959650, 571611264412717551

Offset

1,2

Links

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

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

Formula

a(n) = 7*a(n-1) + a(n-3) - 7*a(n-4).

G.f.: x*(1 + x^2)/((1 - x)*(1 - 7*x)*(1 + x + x^2)). - Colin Barker, Dec 24 2015

From Stefano Spezia, Mar 31 2023: (Start)

E.g.f.: exp(-x/2)*(exp(3*x/2)*(25*exp(6*x) - 19) - 6*cos(sqrt(3)*x/2) + 8*sqrt(3)*sin(sqrt(3)*x/2))/171.

a(n) ~ 25*7^n/171. (End)

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 0, 1}], 7], {n, 30}] (* or *) LinearRecurrence[ {7, 0, 1, -7}, {1, 7, 50, 351}, 30] (* Harvey P. Dale, Feb 04 2019 *)

Prog

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

Crossrefs

Cf. A000420.

Sequence in context: A288787 A033117 A096882 * A022037 A054413 A163458

Adjacent sequences: A033122 A033123 A033124 * A033126 A033127 A033128

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved