A037488 Base 3 digits are, in order, the first n terms of the periodic sequence with initial period 2,1.

2, 7, 23, 70, 212, 637, 1913, 5740, 17222, 51667, 155003, 465010, 1395032, 4185097, 12555293, 37665880, 112997642, 338992927, 1016978783, 3050936350, 9152809052, 27458427157, 82375281473, 247125844420, 741377533262

Offset

1,1

Links

Table of n, a(n) for n=1..25.

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

Formula

a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3).

G.f.: x*(2+x)/((1-x^2)*(1-3*x)). - Michael Somos, Sep 28 2002

a(n) = (7*3^n-(-1)^n-6)/8. - Bruno Berselli, Jan 20 2011

Mathematica

Module[{nn=30, c}, c=PadRight[{}, nn, {2, 1}]; Table[FromDigits[Take[c, n], 3], {n, nn}]] (* or *) LinearRecurrence[{3, 1, -3}, {2, 7, 23}, 30] (* Harvey P. Dale, May 21 2015 *)

Prog

(PARI) a(n)=if(n<1, 0, 3*a(n-1)+1+n%2)
(PARI) a(n)=if(n<1, 0, 3^n*7\8)

Crossrefs

Sequence in context: A048496 A369840 A210581 * A129669 A037568 A076656

Adjacent sequences: A037485 A037486 A037487 * A037489 A037490 A037491

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved