A309792 Expansion of (2 + 6*x + 3*x^2 +4*x^3 - 10*x^4)/(1 - x - 4*x^4 + 4*x^5).

2, 8, 5, 9, 7, 31, 19, 35, 27, 123, 75, 139, 107, 491, 299, 555, 427, 1963, 1195, 2219, 1707, 7851, 4779, 8875, 6827, 31403, 19115, 35499, 27307, 125611, 76459, 141995, 109227, 502443, 305835, 567979, 436907, 2009771, 1223339, 2271915, 1747627, 8039083, 4893355, 9087659, 6990507, 32156331

Offset: 0

Author

Georg Fischer, Aug 17 2019

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,4,-4).

Crossrefs

Cf. A307048, A309791.

Programs

Mathematica

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

Formula

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