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A085750 Determinant of the symmetric n X n matrix A defined by A[i,j] = |i-j| for 1 <= i,j <= n. 12
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, 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

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Last modified November 22 08:57 EST 2017. Contains 295076 sequences.