A037532 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,2.

1, 8, 58, 407, 2850, 19952, 139665, 977656, 6843594, 47905159, 335336114, 2347352800, 16431469601, 115020287208, 805142010458, 5635994073207, 39451958512450, 276163709587152, 1933145967110065

Offset

1,2

Links

Table of n, a(n) for n=1..19.

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

Formula

G.f.: x*(1+x+2*x^2) / ( (x-1)*(7*x-1)*(1+x+x^2) ). - R. J. Mathar, Apr 29 2015

a(n) = 5/57*A049347(n-1) + 3/57*A049347(n) + 29/171*A000420(n) - 2/9. - Enxhell Luzhnica, Apr 27 2016

a(n) = (29*7^n + 7*sqrt(3)*sin(2*Pi*n/3) + 9*cos(2*Pi*n/3) - 38)/171. - Ilya Gutkovskiy, Apr 27 2016

Mathematica

Rest@ CoefficientList[Series[x (1 + x + 2 x^2)/((x - 1) (7 x - 1) (1 + x + x^2)), {x, 0, 19}], x] (* Michael De Vlieger, Apr 28 2016 *)

Prog

(PARI) Vec(x*(1+x+2*x^2) / ( (x-1)*(7*x-1)*(1+x+x^2) ) + O(x^30)) \\ Michel Marcus, Apr 28 2016

Crossrefs

Sequence in context: A125371 A162272 A273584 * A062236 A178730 A190978

Adjacent sequences: A037529 A037530 A037531 * A037533 A037534 A037535

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved