A033143 Base-7 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0.

1, 7, 49, 344, 2408, 16856, 117993, 825951, 5781657, 40471600, 283301200, 1983108400, 13881758801, 97172311607, 680206181249, 4761443268744, 33330102881208, 233310720168456, 1633175041179193, 11432225288254351, 80025577017780457, 560179039124463200, 3921253273871242400

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

a(n) = floor(7^(n+2)/342). - Christian Krause, May 19 2026

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 0, 0}], 7], {n, 30}] (* Harvey P. Dale, Mar 28 2025 *)
(* Alternative: *)
LinearRecurrence[{7, 0, 1, -7}, {1, 7, 49, 344}, 30] (* Harvey P. Dale, Mar 28 2025 *)

Prog

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

Crossrefs

Sequence in context: A373283 A050737 A195908 * A388410 A024582 A024587

Adjacent sequences: A033140 A033141 A033142 * A033144 A033145 A033146

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Status

approved