A106202 Expansion of Im(x/(1 - x - 2*i*x^2)), i=sqrt(-1).

0, 0, 0, 2, 4, 6, 8, 2, -20, -66, -144, -230, -236, 22, 856, 2610, 5308, 7918, 7104, -4150, -36636, -100794, -193368, -269342, -198772, 274974, 1522192, 3846778, 6966452, 8986230, 4917240, -14538862, -61860772, -145127602, -248063392, -292843734, -90180988, 692992166, 2468418888, 5415220546, 8722746156, 9258303102

Offset: 0

Author

Paul Barry, Apr 25 2005

Keywords

• easy
• sign

Comments

Real part is A106201.

For n>=2, a(n) equals -1 times the imaginary part of the determinant of the (n-1) X (n-1) matrix with i's along the superdiagonal (i is the imaginary unit), 2's along the subdiagonal, 1's along the main diagonal, and 0's everywhere else (see Mathematica code below). - John M. Campbell, Jun 04 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,-4).

Crossrefs

Cf. A001045, A014292, A104862.

Programs

Mathematica

Table[-Im[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {n - 1, n - 1}] + Array[KroneckerDelta[#1 - 1, #2]*2 &, {n - 1, n - 1}] + IdentityMatrix[n - 1]]], {n, 2, 40}] (* John M. Campbell, Jun 04 2011 *)

PARI

concat(vector(3), Vec(2*x^3/(1-2*x+x^2+4*x^4) + O(x^50))) \\ Michel Marcus, Jan 03 2016

Formula

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

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k)*2^k*sin(Pi*k/2).