A216034 - OEIS

%I #22 Feb 17 2024 06:28:56

%S 1,1,11,35,115,1129,3697,12105,118907,389339,1274819,12522481,

%T 41002561,134255345,1318783307,4318113395,14138868147,138885370201,

%U 454754601649,1489010307001,14626471197755,47891689912619,156812530628611,1540361374197601

%N a(n) = 3^(-1+floor((n+1)/3))*A(n), where A(n) = 3*A(n-1) + A(n-2) - A(n-3)/3 with A(0)=A(1)=3, A(2)=11.

%C The Berndt-type sequence number 11a for the argument 2Pi/9 - see A215945 for more details.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,105,0,0,33,0,0,-1).

%F G.f.: (1+x+11*x^2-70*x^3+10*x^4-26*x^5-11*x^6-3*x^7-x^8)/(1-105*x^3-33*x^6+x^9). [_Bruno Berselli_, Oct 02 2012]

%o (Magma) i:=24; I:=[3,3,11]; A:=[m le 3 select I[m] else 3*Self(m-1)+Self(m-2)-Self(m-3)/3: m in [1..i]]; [3^(-1+Floor(n/3))*A[n]: n in [1..i]]; // _Bruno Berselli_, Oct 02 2012

%Y Cf. A215945, A215948, A215829, A215794, A215575.

%K nonn,easy

%O 0,3

%A _Roman Witula_, Aug 30 2012