A074081 Sum of determinants of 3rd-order principal minors of powers of inverse of tetramatrix ((1,1,0,0),(1,0,1,0),(1,0,0,1),(1,0,0,0)).

4, -1, 3, -7, 15, -26, 51, -99, 191, -367, 708, -1365, 2631, -5071, 9775, -18842, 36319, -70007, 134943, -260111, 501380, -966441, 1862875, -3590807, 6921503, -13341626, 25716811, -49570747, 95550687, -184179871, 355018116, -684319421, 1319068095, -2542585503, 4900991135

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 19 2002

Keywords

• easy
• sign

Links

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

Crossrefs

Cf. A073817.

Programs

Mathematica

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

Formula

a(n) = (-1)^n*T(n), where T(n) are the generalized tetranacci numbers A073817.

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

G.f.: (4+3x-2x^2+x^3)/(1+x-x^2+x^3-x^4).