login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085750 Determinant of the symmetric n X n matrix A defined by A[i,j] = |i-j| for 1 <= i,j <= n. 15
0, -1, 4, -12, 32, -80, 192, -448, 1024, -2304, 5120, -11264, 24576, -53248, 114688, -245760, 524288, -1114112, 2359296, -4980736, 10485760, -22020096, 46137344, -96468992, 201326592, -419430400, 872415232, -1811939328, 3758096384, -7784628224, 16106127360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The determinant of the distance matrix of a tree with vertex set {1,2,...,n}. The distance matrix is the n X n matrix in which the (i,j)-term is the number of edges in the unique path from vertex i to vertex j. [The matrix A in the definition is the distance matrix of the path-tree 1-2-...-n.]

Hankel transform of A100071. Also Hankel transform of C(2n-2,n-1)(-1)^(n-1). Inverse binomial transform of -n. - Paul Barry, Jan 11 2007

Pisano period lengths: 1, 1, 3, 1, 20, 3, 42, 1, 9, 20, 55, 3,156, 42, 60, 1,136, 9,171, 20, ... - R. J. Mathar, Aug 10 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

R. L. Graham and H. O. Pollak, On the addressing problem for loop switching, Bell System Tech. J., 50, 1971, 2495-2519.

Tanya Khovanova, Recursive Sequences

R. Merris, The distance spectrum of a tree, J. Graph Theory, 14, No. 3, 1990,365-369.

Index entries for linear recurrences with constant coefficients, signature (-4,-4)

FORMULA

a(n) = (-1)^(n+1) * (n-1) * 2^(n-2) = (-1)^(n+1) * A001787(n-1).

G.f.: -x/(1+2x)^2. - Paul Barry, Jan 11 2007

a(n) = -4*a(n-1) - 4*a(n-2); a(1)=0, a(1)=-1. - Philippe Deléham, Nov 03 2008

MAPLE

seq((-1)^(n-1)*(n-1)*2^(n-2), n = 1 .. 31);

MATHEMATICA

Table[-(-1)^n*2^(n - 2)*(n - 1), {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 10 2011 *)

LinearRecurrence[{-4, -4}, {0, -1}, 40] (* Harvey P. Dale, Apr 14 2014 *)

CoefficientList[Series[-x/(1 + 2 x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 15 2014 *)

CROSSREFS

Essentially the same as A001787.

Cf. A085807, A203993, A204249, A278845, A278847.

Sequence in context: A260186 A097067 A139756 * A001787 A118442 A038592

Adjacent sequences:  A085747 A085748 A085749 * A085751 A085752 A085753

KEYWORD

sign

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 21 2003

EXTENSIONS

More terms from Philippe Deléham, Nov 16 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 02:56 EST 2020. Contains 338899 sequences. (Running on oeis4.)