A037579 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 10, 71, 500, 3501, 24510, 171571, 1201000, 8407001, 58849010, 411943071, 2883601500, 20185210501, 141296473510, 989075314571, 6923527202000, 48464690414001, 339252832898010, 2374769830286071, 16623388812002500, 116363721684017501, 814546051788122510

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (5*7^n-3*(-1)^(n-1)-8)/24. a(n) = 7*a(n-1)+a(n-2)-7*a(n-3). G.f.: x*(3*x+1) / ((x-1)*(x+1)*(7*x-1)). - Colin Barker, Dec 27 2012; corrected Apr 30 2014

Maple

A037579:=n->(5*7^n-3*(-1)^(n-1)-8)/24; seq(A037579(n), n=1..30); # Wesley Ivan Hurt, Apr 29 2014

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (7 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
Table[FromDigits[PadRight[{}, n, {1, 3}], 7], {n, 30}] (* or *) LinearRecurrence[ {7, 1, -7}, {1, 10, 71}, 30] (* Harvey P. Dale, Dec 29 2019 *)

Prog

(Magma) [(5*7^n-3*(-1)^(n-1)-8)/24: n in [1..30]]; // Vincenzo Librandi, Oct 22 2013

Crossrefs

Sequence in context: A129275 A049672 A221548 * A166791 A271035 A108276

Adjacent sequences: A037576 A037577 A037578 * A037580 A037581 A037582

Keyword

nonn,base,easy

Author

Clark Kimberling, Dec 11 1999

Extensions

More terms from Colin Barker, Dec 27 2012

Status

approved