

A085750


Determinant of the symmetric n X n matrix A defined by A[i,j] = ij 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
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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 pathtree 12...n.]
Hankel transform of A100071. Also Hankel transform of C(2n2,n1)(1)^(n1). 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, 24952519.
Tanya Khovanova, Recursive Sequences
R. Merris, The distance spectrum of a tree, J. Graph Theory, 14, No. 3, 1990,365369.
Index entries for linear recurrences with constant coefficients, signature (4,4)


FORMULA

a(n) = (1)^(n+1) * (n1) * 2^(n2) = (1)^(n+1) * A001787(n1).
G.f.: x/(1+2x)^2.  Paul Barry, Jan 11 2007
a(n) = 4*a(n1)  4*a(n2); a(1)=0, a(1)=1.  Philippe Deléham, Nov 03 2008


MAPLE

seq((1)^(n1)*(n1)*2^(n2), 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



