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A028361
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Totally isotropic spaces of index n in orthogonal geometry of dimension 2n.
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13
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1, 2, 6, 30, 270, 4590, 151470, 9845550, 1270075950, 326409519150, 167448083323950, 171634285407048750, 351678650799042888750, 1440827432323678715208750, 11804699153027899713705288750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| These numbers appear in first column of A155103. [From Mats Granvik (mats.granvik(AT)abo.fi), Jan 20 2009]
Equals row sums of unsigned triangle A158474 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 02 2010: (Start)
a(n) = (n+2) terms in the sequence (1, 1, 2, 4, 8, 16,...) dot (n+2) terms
in the sequence (1, 1, 2, 6, 30, 270,...). Example: a(4) = 4590 =
(1, 2, 4, 8, 16) dot (1, 1, 2, 6, 30, 270) = (1 + 1 + 4 + 24 + 240 + 4230). (End)
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REFERENCES
| C. Bachoc and P. Gaborit, On extremal additive F_4 codes of length 10 to 18, J. Theorie Nombres Bordeaux, 12 (2000), 255-271.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
| Product( 2^i+1, i=0..n-1) (n>0).
Asymptotic to C*2^(n*(n-1)/2) where C=4.76846205806274344829979857....=prod(k>=0, 1+1/2^k) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 09 2003
It appears that a(n) = 2^((1/2)*(n - 1)*n) * prod(1 + 1/(2^k), k >= 0) / prod(1 + 1/(2^(n + k)), k >= 0) [From Peter Moxey (pmoxey(AT)live.com), Mar 21 2010]
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CROSSREFS
| A028362.
Cf. A155103. [From Mats Granvik (mats.granvik(AT)abo.fi), Jan 20 2009]
Cf. A158474 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009]
Sequence in context: A097385 A066068 A121406 * A106339 A120295 A071350
Adjacent sequences: A028358 A028359 A028360 * A028362 A028363 A028364
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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