A075270 Sum of Lucas numbers and inverted Lucas numbers: a(n) = A000032(n)*A075193(n).

3, -2, 7, -3, 18, -7, 47, -18, 123, -47, 322, -123, 843, -322, 2207, -843, 5778, -2207, 15127, -5778, 39603, -15127, 103682, -39603, 271443, -103682, 710647, -271443, 1860498, -710647, 4870847, -1860498, 12752043, -4870847, 33385282, -12752043, 87403803, -33385282, 228826127, -87403803

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 12 2002

Keywords

• easy
• sign

Comments

a(n) = (1 + (-1)^n)*L(n) + ((-1)^n)*L(n-1), L(n) Lucas numbers.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

Crossrefs

Cf. A000032, A075193.

Programs

Mathematica

CoefficientList[Series[(3-2x-2x^2+3x^3)/(1-3x^2+x^4), {x, 0, 40}], x]

Formula

a(n) = 3*a(n-2) - a(n-4); a(0)=3, a(1)=-2, a(2)=7, a(3)=-3.

O.g.f. (3-2*x-2*x^2+3*x^3)/(1-3*x^2+x^4).