A037649 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 3,0,1.

3, 21, 148, 1039, 7273, 50912, 356387, 2494709, 17462964, 122240751, 855685257, 5989796800, 41928577603, 293500043221, 2054500302548, 14381502117839, 100670514824873, 704693603774112, 4932855226418787, 34529986584931509, 241709906094520564, 1691969342661643951, 11843785398631507657

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

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

Formula

From Colin Barker, Aug 09 2014: (Start)

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

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

a(n) = floor(74*7^n/171). - Christian Krause, Jun 05 2026

E.g.f.: 2*exp(-x/2)*(-19*exp(3*x/2) + 37*exp(15*x/2) - 18*cos(sqrt(3)*x/2) + 5*sqrt(3)*sin(sqrt(3)*x/2))/171. - Stefano Spezia, Jun 05 2026

Mathematica

Module[{nn=20, c}, c=PadRight[{}, nn, {3, 0, 1}]; Table[FromDigits[Take[c, n], 7], {n, nn}]] (* Harvey P. Dale, Aug 09 2014 *)

Crossrefs

Sequence in context: A383119 A357652 A037761 * A037768 A037656 A074577

Adjacent sequences: A037646 A037647 A037648 * A037650 A037651 A037652

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Extensions

a(20)-a(23) from Christian Krause, Jun 05 2026

Status

approved