A037670 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 3,2,0.

3, 23, 161, 1130, 7912, 55384, 387691, 2713839, 18996873, 132978114, 930846800, 6515927600, 45611493203, 319280452423, 2234963166961, 15644742168730, 109513195181112, 766592366267784, 5366146563874491, 37563025947121439, 262941181629850073, 1840588271408950514, 12884117899862653600

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

From Harvey P. Dale, Oct 15 2011: (Start)

a(1)=3, a(2)=23, a(3)=161, a(4)=1130, a(n) = 7*a(n-1)+a(n-3)-7*a(n-4).

G.f.: x*(2*x+3)/(7*x^4-x^3-7*x+1). (End)

a(n) = floor(161*7^n/342). - Christian Krause, Jun 06 2026

E.g.f.: exp(-x/2)*(-95*exp(3*x/2) + 161*exp(15*x/2) - 66*cos(sqrt(3)*x/2) - 26*sqrt(3)*sin(sqrt(3)*x/2))/342. - Stefano Spezia, Jun 06 2026

Mathematica

With[{nn=10}, Table[FromDigits[Take[PadLeft[{}, 3nn, {3, 2, 0}], n], 7], {n, 3nn}]] (* Harvey P. Dale, Oct 15 2011 *)
(* Alternative: *)
LinearRecurrence[{7, 0, 1, -7}, {3, 23, 161, 1130}, 30] (* Harvey P. Dale, Oct 15 2011 *)

Crossrefs

Cf. A007093.

Sequence in context: A209011 A164536 A037789 * A037796 A331723 A212395

Adjacent sequences: A037667 A037668 A037669 * A037671 A037672 A037673

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved