|
| |
|
|
A106202
|
|
Expansion of Im(x/(1-x-2*i*x^2)), i=sqrt(-1).
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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 (jmaxwellcampbell(AT)gmail.com), June 4 2011]
|
|
|
FORMULA
| G.f.: 2*x^3/(1-2*x+x^2+4*x^4).
a(n) = sum(k=0..floor((n-1)/2), C(n-k-1, k)*2^k*sin(pi*k/2) ).
|
|
|
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}] (* From John M. Campbell (jmaxwellcampbell(AT)gmail.com), June 4 2011 *)
|
|
|
CROSSREFS
| Cf. A104862, A014292, A001045.
Sequence in context: A004519 A036839 A004093 * A179657 A064745 A115425
Adjacent sequences: A106199 A106200 A106201 * A106203 A106204 A106205
|
|
|
KEYWORD
| easy,sign
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 25 2005
|
| |
|
|
