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A062741
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3 times pentagonal numbers: 3*n*(3*n-1)/2.
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21
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=C(3*n,2),n>=0. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
a(n) = (9*n^2-3*n)/2 = 3*n(3*n-1)/2 = A000326(n)*3. [From Omar E. Pol (info(AT)polprimos.com), Dec 11 2008]
a(n)=9*n+a(n-1)-6 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
G.f.: 3*x*(1+2*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
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EXAMPLE
| The spiral begins:
..........15
........16..14
......17..3...13
....18..4...2...12
..19..5...0...1...11
20..6...7...8...9...10
a(1)=9*1+0-6=3; a(2)=9*2+3-6=15; a(3)=9*3+15-6=36 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MAPLE
| [seq(binomial(3*n, 2), n=0..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
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MATHEMATICA
| 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
| Cf. A051682, A000326.
3 times n-gonal numbers: A045943, A033428, A094159, A152773, A152751, A152759, A152767, A153783, A153448, A153875.- Bruno Berselli, Jan 21 2011
Sequence in context: A162441 A001803 A161738 * A185541 A176661 A117561
Adjacent sequences: A062738 A062739 A062740 * A062742 A062743 A062744
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KEYWORD
| nonn,easy
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001
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EXTENSIONS
| Better definition and edited. - Omar E. Pol (info(AT)polprimos.com), Dec 11 2008
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