A037618 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,3.

2, 8, 35, 142, 568, 2275, 9102, 36408, 145635, 582542, 2330168, 9320675, 37282702, 149130808, 596523235, 2386092942, 9544371768, 38177487075, 152709948302, 610839793208, 2443359172835, 9773436691342, 39093746765368

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy
• changed

Links

• Index entries for 2-automatic sequences.
• Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4)

Programs

Mathematica

Table[FromDigits[PadRight[{},n,{2,0,3}],4],{n,30}] (* or *) LinearRecurrence[{4,0,1,-4},{2,8,35,142},30] (* Harvey P. Dale, Aug 23 2025 *)

PARI

a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -4,1,0,4]^(n-1)*[2;8;35;142])[1,1] \\ Charles R Greathouse IV, Feb 13 2017

Formula

G.f.: x*(2+3*x^2) / ( (x-1)*(4*x-1)*(1+x+x^2) ). - R. J. Mathar, Apr 27 2015

A007090(a(n)) = A037624(n). - R. J. Mathar, Apr 27 2015