%I #20 Dec 12 2023 07:41:45

%S 1,81,81,3,81,81,9,81,81,3,81,81,3,81,81,9,81,81,3,81,81,1,81,81,9,81,

%T 81,1,81,81,3,81,81,9,81,81,3,81,81,3,81,81,9,81,81,3,81,81,1,81,81,9,

%U 81,81,1,81,81,3,81,81,9,81,81,3,81,81,3,81,81,9,81,81,3,81,81,1,81,81

%N Period 27: repeat 1, 81, 81, 3, 81, 81, 9, 81, 81, 3, 81, 81, 3, 81, 81, 9, 81, 81, 3, 81, 81, 1, 81, 81, 9, 81, 81.

%C The generating formula is a(n) = A061040(n+3) - 9*A061039(n+3). This is a member of the family of sequences with A000012(n) = A000290(n+1) -A005563(n+1), with period length 1, and A177499(n) = A061038(n+2) -4*A061037(n+2), with period length 4.

%C a(n) here has period length 3^3 and the general series of this family has period length k^k.

%H <a href="/index/Rec#order_27">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%F G.f.: ( -1 -81*x -3*x^9 -3*x^3 -81*x^4 -81*x^5 -9*x^6 -81*x^7 -81*x^8 -81*x^10 -3*x^12 -81*x^13 -81*x^14 -9*x^15 -81*x^16 -81*x^17 -3*x^18 -81*x^19 -81*x^20 -x^21 -81*x^22 -81*x^23 -9*x^24 -81*x^25 -81*x^26 -81*x^11 -81*x^2 ) / ( (x-1) *(1+x+x^2) *(1+x^3+x^6) *(1+x^9+x^18) ). - _R. J. Mathar_, Dec 09 2010

%F a(n) = a(n+27).

%o (PARI) a(n)=3^[0, 4, 4, 1, 4, 4, 2, 4, 4, 1, 4, 4, 1, 4, 4, 2, 4, 4, 1, 4, 4, 0, 4, 4, 2, 4, 4][n%27+1] \\ _Charles R Greathouse IV_, Jul 17 2016

%K nonn,easy

%O 0,2

%A _Paul Curtz_, May 14 2010