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A060344 For n >= 2, let N_n denote the set of all unipotent upper-triangular real n X n matrices A such that for every k=1,2,...,n-1 the minor of A with rows 1,2,...,k and columns n-k+1,...,n is nonzero. a(n) is the number of connected components of N_n. 2
2, 6, 20, 52, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

REFERENCES

B. Shapiro, M. Shapiro and A. Vainshtein, Connected components in the intersection of two open opposite Schubert cells in SL_n/B, Internat. Math. Res. Notices, 1997, no. 10, pp. 469-493.

B. Shapiro, M. Shapiro and A. Vainshtein, Skew-symmetric vanishing lattices and intersections of Schubert cells. Internat. Math. Res. Notices, 1998, no. 11, pp. 563-588.

LINKS

Harry J. Smith, Table of n, a(n) for n = 2..500

FORMULA

a(2)=2, a(3)=6, a(4)=20, a(5)=52; for n > 5, a(n) = 3 * 2^(n-1).

G.f.: 2*x^2*(1 + x + 4*x^2 + 6*x^3 - 4*x^4)/(1 - 2*x). - Colin Barker, Mar 08 2012

EXAMPLE

a(2) = 2 because in this case the set N_n is topologically just the set of nonzero real numbers so the number of components is 2.

MATHEMATICA

Join[{2, 6, 20, 52}, Table[3 2^(n-1), {n, 6, 40}]] (* Harvey P. Dale, Mar 09 2014 *)

PROG

(PARI) { for (n=2, 500, a=3*2^(n - 1); if (n==2, a=2); if (n==3, a=6); if (n==4, a=20); if (n==5, a=52); write("b060344.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 04 2009

CROSSREFS

Cf. A003945.

Sequence in context: A027558 A320910 A066397 * A045655 A303307 A321192

Adjacent sequences:  A060341 A060342 A060343 * A060345 A060346 A060347

KEYWORD

nonn,easy

AUTHOR

Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001

EXTENSIONS

More terms from Harry J. Smith, Jul 04 2009

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)