A087170 Expansion of (1 + 4*x)/(1 + 7*x + 16*x^2).

1, -3, 5, 13, -171, 989, -4187, 13485, -27403, -23939, 606021, -3859123, 17317525, -59476707, 139256549, -23168531, -2065925067, 14832171965, -70770402683, 258078067341, -674220028459, 590291121757, 6655482603045, -56033036169427, 285743531537269, -1103676142050051

Offset

0,2

Comments

For positive n, a(n) equals 4^n times the permanent of the (2n) X (2n) matrix with 1/2's along the main diagonal, and i's along the superdiagonal and the subdiagonal (where i is the imaginary unit). - John M. Campbell, Jul 08 2011

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (-7,-16).

Formula

G.f.: (1 + 4*x)/(1 + 7*x + 16*x^2).

a(n) = -7*a(n-1) - 16*a(n-2), a(0)=1, a(1)=-3.

a(n) = Sum_{k=0..n} binomial(n+k,2*k)*(-4)^(n-k).

Mathematica

CoefficientList[Series[(1 + 4x)/(16x^2 + 7x + 1), {x, 0, 25}], x]

Crossrefs

Sequence in context: A155012 A121533 A187733 * A123370 A110407 A340037

Adjacent sequences: A087167 A087168 A087169 * A087171 A087172 A087173

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2003

Status

approved