%I #12 Apr 19 2023 02:41:12

%S 2,8,5,9,7,31,19,35,27,123,75,139,107,491,299,555,427,1963,1195,2219,

%T 1707,7851,4779,8875,6827,31403,19115,35499,27307,125611,76459,141995,

%U 109227,502443,305835,567979,436907,2009771,1223339,2271915,1747627,8039083,4893355,9087659,6990507,32156331

%N Expansion of (2 + 6*x + 3*x^2 +4*x^3 - 10*x^4)/(1 - x - 4*x^4 + 4*x^5).

%C This sequence is used for maps which are derived from the table in A307048, and which are described in the companion sequence A309791.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,4,-4).

%F a(n) = (1/12)*(4+2^(n/2)*(12*(1+(-1)^n)-2*(-i)^n+18*sqrt(2)*(1-(-1)^n)+5*i*(-i)^n*sqrt(2)-i^(n+1)*(-2*i+5*sqrt(2)))), where i = sqrt(-1). - _Stefano Spezia_, Aug 19 2019

%t LinearRecurrence[{1, 0, 0, 4, -4}, {2, 8, 5, 9, 7}, 40] (* or *)

%t CoefficientList[Series[(2 + 6*x + 3*x^2 +4*x^3 - 10*x^4)/(1 - x - 4*x^4 + 4*x^5), {x, 0, 40}], x]

%Y Cf. A307048, A309791.

%K nonn,easy

%O 0,1

%A _Georg Fischer_, Aug 17 2019