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Search: id:A033428
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| 0, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 363, 432, 507, 588, 675, 768, 867, 972, 1083, 1200, 1323, 1452, 1587, 1728, 1875, 2028, 2187, 2352, 2523, 2700, 2883, 3072, 3267, 3468, 3675, 3888, 4107, 4332, 4563, 4800, 5043, 5292, 5547, 5808, 6075, 6348
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The number of edges of a complete tripartite graph of order 3n, K_n,n,n. - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Oct 18 2001
Write 1,2,3,4,... in a hexagonal spiral around 0, then a(n) is the sequence found by reading the line from 0 in the direction 0,3,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:
......16..15..14
....17..5...4...13
..18..6...0...3...12
19..7...1...2...11..26
..20..8...9...10..25
....21..22..23..24
Number of edges of the complete bipartite graph of order 4n, K_n,3n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Also the number of partitions of 6n + 3 into at most 3 parts.- R. K. Guy, Oct 23, 2003
Number of permutations of 3 distinct letters (ABC) each with n copies such that 3n-2 remain fixed points. E.g. if AAAAABBBBBCCCCC (3*5=15 letters) then 15-2=13 fixed points n5=75 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 02 2006
Numbers n such that the imaginary quadratic field Q[Sqrt[ -n]] has six units. - Marc LeBrun (mlb(AT)well.com), Apr 12 2006
The denominators of Hoehn's sequence (recalled by G. L. Honaker, Jr.) and the numerators of that sequence reversed. The sequence is 1/3, (1+3)/(5+7), (1+3+5)/(7+9+11), (1+3+5+7)/(9+11+13+15), . . . ; reduced to 1/3, 4/12, 9/27, 16/48, . . . . For the reversal, the reduction is 3/1, 12/4, 27/9, 48/16, . . . . - Enoch Haga (Enokh(AT)comcast.net), Oct 05 2007
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LINKS
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F. Ellermann, Illustration of binomial transforms
Eric Weisstein's World of Mathematics, Unit
E. Weisstein, Numbers of units in imaginary quadratic fields
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FORMULA
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a(n)= A049452(n)-A049450(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
Right edge of the triangle in A132111: a(n)=A132111(n,n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2007
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MAPLE
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seq(n*(6*n-1)-n*(3*n-1), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
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PROGRAM
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(PARI) a(n)=3*n^2
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CROSSREFS
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Cf. A000567, A000217, A000290, A033581, A033583.
a(n)=3*A000290(n)
Cf. A033581.
Cf. A000290, A092205, A092206.
Cf. A000290.
Sequence in context: A125614 A061936 A074630 this_sequence A018230 A058034 A009259
Adjacent sequences: A033425 A033426 A033427 this_sequence A033429 A033430 A033431
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KEYWORD
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nonn
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AUTHOR
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Jeff Burch (jmburch(AT)osprey.smcm.edu)
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EXTENSIONS
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Better description from njas 5/98.
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