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A049450
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Pentagonal numbers multiplied by 2: n*(3*n-1).
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27
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0, 2, 10, 24, 44, 70, 102, 140, 184, 234, 290, 352, 420, 494, 574, 660, 752, 850, 954, 1064, 1180, 1302, 1430, 1564, 1704, 1850, 2002, 2160, 2324, 2494, 2670, 2852, 3040, 3234, 3434, 3640, 3852, 4070, 4294, 4524, 4760, 5002, 5250, 5504, 5764
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 0,2,... - 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
Starting with offset 1 = binomial transform of [2, 8, 6, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
Number of possible pawn moves on an (n+1) X (n+1) chessboard (n=>3). [From Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 04 2010.]
a(n) = A069905(6n-1): Number of partitions of 6*n-1 into 3 parts. [Adi Dani, Jun 04 2011]
Even octagonal numbers divided by 4. - Omar E. Pol, Aug 19 2011
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: A(x) = 2*x*(1+2*x)/(1-x)^3.
a(n)= A049452(n)-A033428(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
a(n)= 2*A000326(n), twice pentagonal numbers. - Omar E. Pol (info(AT)polprimos.com), May 14 2008
a(n) = A022264(n) - A000217(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 09 2008]
a(n)=6*n+a(n-1)-4 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
a(n) = A014642(n)/4 = A033579(n)/2. - Omar E. Pol, Aug 19 2011
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EXAMPLE
| On a 4 x 4 chessboard pawns at the second row have (3+4+4+3) moves and pawns at the third row have (2+3+3+2) moves so a(3) = 24. [From Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 04 2010.]
From Adi Dani, Jun 04 2011: (Start)
a(1)=2: the partitions of 6*1-1=5 into 3 parts are [1,1,3] and[1,2,2].
a(2)=10: the partitions of 6*2-1=11 into 3 parts are [1,1,9], [1,2,8], [1,3,7], [1,4,6], [1,5,5], [2,2,7], [2,3,6], [2,4,5], [3,3,5], and [3,4,4].
(End)
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MAPLE
| seq(n*(3*n-1), n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
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MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(3*n-1)], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
| Cf. A000567.
Bisection of A001859. Cf. A045944, A000326, A033579, A027599, A049451.
Cf. A033586 (King), A035005 (Queen), A035006 (Rook), A035008 (Knight) and A002492 (Bishop). [From Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 04 2010.]
Sequence in context: A005962 A120548 A120845 * A092906 A130016 A120550
Adjacent sequences: A049447 A049448 A049449 * A049451 A049452 A049453
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Joe Keane (jgk(AT)jgk.org).
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EXTENSIONS
| Comment, example and crossrefs added and minor errors corrected by Johannes W. Meijer (meijgia(AT)hotmail.com), Feb 04 2010
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