A037496 Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,2.

1, 3, 11, 34, 102, 308, 925, 2775, 8327, 24982, 74946, 224840, 674521, 2023563, 6070691, 18212074, 54636222, 163908668, 491726005, 1475178015, 4425534047, 13276602142, 39829806426, 119489419280, 358468257841, 1075404773523

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,0,1,-3).

Programs

Magma

I:=[1,3,11,34]; [n le 4 select I[n] else 3*Self(n-1) +Self(n-3)-3*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 26 2016

Mathematica

With[{c=PadRight[{},30,{1,0,2}]},Table[FromDigits[Take[c,n],3],{n,30}]] (* or *) LinearRecurrence[{3,0,1,-3},{1,3,11,34},30] (* Harvey P. Dale, Mar 30 2012 *)

Formula

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

From Bruno Berselli, Jan 20 2011: (Start)

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

a(n) = round((11*3^n-13)/26) = (11*3^n-13)/26 + ((3-7*i*sqrt(3))*(-1+i*sqrt(3))^n + (3+7*i*sqrt(3))*(-1-i*sqrt(3))^n)/(78*2^n) where i is the imaginary unit. (End)