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

0,1

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

Table of n, a(n) for n=0..45.

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

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

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]

Crossrefs

Cf. A307048, A309791.

Sequence in context: A271886 A182528 A185583 * A318725 A155901 A029745

Adjacent sequences: A309789 A309790 A309791 * A309793 A309794 A309795

Keyword

nonn,easy

Author

Georg Fischer, Aug 17 2019

Status

approved