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Search: id:A062741
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| A062741 |
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Pentagonal numbers multiplied by 3. |
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+0
7
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| 0, 3, 15, 36, 66, 105, 153, 210, 276, 351, 435, 528, 630, 741, 861, 990, 1128, 1275, 1431, 1596, 1770, 1953, 2145, 2346, 2556, 2775, 3003, 3240, 3486, 3741, 4005, 4278, 4560, 4851, 5151, 5460, 5778, 6105, 6441, 6786, 7140, 7503, 7875, 8256, 8646, 9045
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading from 0 in the vertical upward direction.
Number of edges in the join of two complete graphs of order 2n and n, K_2n * K_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
3 times pentagonal numbers. [From Omar E. Pol (info(AT)polprimos.com), Dec 14 2008]
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FORMULA
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a(n) = n*(9n-3)/2
a(n)=C(3*n,2),n>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
a(n) = (9n^2-3n)/2 = 3n(3n-1)/2 = A000326(n)*3. [From Omar E. Pol (info(AT)polprimos.com), Dec 11 2008]
a(n)=9*n+a(n-1)-15 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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The spiral begins:
..........15
........16..14
......17..3...13
....18..4...2...12
..19..5...0...1...11
20..6...7...8...9...10
For n=2, a(2)=9*2+0-15=3; n=3, a(3)=9*3+3-15=15; n=4, a(4)=9*4+15-15=36 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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MAPLE
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[seq(binomial(3*n, 2), n=0..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +3; AppendTo[lst, s], {n, 0, 6!, 9}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
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Cf. A051682.
Cf. A000326. [From Omar E. Pol (info(AT)polprimos.com), Dec 11 2008]
Sequence in context: A162441 A001803 A161738 this_sequence A117561 A065765 A146853
Adjacent sequences: A062738 A062739 A062740 this_sequence A062742 A062743 A062744
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KEYWORD
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nonn,easy,new
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001
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EXTENSIONS
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Better definition and edited. - Omar E. Pol (info(AT)polprimos.com), Dec 11 2008
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