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A016283
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6^n/8 - 4^(n-1) + 2^(n-3).
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3
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0, 0, 1, 12, 100, 720, 4816, 30912, 193600, 1194240, 7296256, 44301312, 267904000, 1615810560, 9728413696, 58504691712, 351565004800, 2111537479680, 12677814747136, 76101248090112, 456744927232000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Number of rectangles that can be formed from the vertices of an n-dimensional cube. E.g. a(3)=12 because the three dimensional cube has six faces plus six rectangles passing through the center of the cube. Cf. A064436: each rectangle on the cube provides an opportunity for a function to not be a linear threshold function, by alternating in value around the rectangle. - Matthew Cook (cook(AT)paradise.caltech.edu), Jan 26 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..150
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FORMULA
| a(n) = (2^n)*stirling2(n+3, 3), n>=0, with stirling2(n, m)=A008277(n, m).
G.f.: x^2/((1-2*x)*(1-4*x)*(1-6*x)). E.g.f.: (exp(2*x)-8*exp(4*x)+9*exp(6*x))/2!.
a(n) =((6^n - 2^n)/4-(4^n - 2^n)/2)/2 , n>=0 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
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MAPLE
| [seq(9/2*6^n-4*4^n+1/2*2^n, n=0..20)]; - Detlef Pauly (dettodet(AT)yahoo.de), Dec 04 2001
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PROG
| (Sage) [((6^n - 2^n)/4-(4^n - 2^n)/2)/2 for n in xrange(0, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2009]
(MAGMA) [6^n/8 - 4^(n-1) + 2^(n-3): n in [0..25]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
| Third column of triangle A075497.
Cf. A025966.
Sequence in context: A052178 A123902 A085374 * A199681 A008547 A109020
Adjacent sequences: A016280 A016281 A016282 * A016284 A016285 A016286
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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