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Search: id:A049450
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| A049450 |
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Pentagonal numbers multiplied by 2: n*(3*n-1). |
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+0
22
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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; listen)
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OFFSET
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0,2
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COMMENT
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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
Twice pentagonal numbers. - Omar E. Pol (info(AT)polprimos.com), May 14 2008
Starting with offset 1 = binomial transform of [2, 8, 6, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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G.f.: A(x) = 2*x*(1+2*x)/(1-x)^3.
a(n)= A049452(n)-A033428(n), example: 102=210-108, etc... - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
a(n)=A000326(n)*2. - 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]
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MAPLE
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a:=n->sum(n/3, j=2..n): seq(a(3*n), n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007
seq(n*(3*n-1), n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
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MATHEMATICA
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lst={}; Do[AppendTo[lst, n*(3*n-1)], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 1, 6!, 6}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
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CROSSREFS
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Cf. A000567.
Bisection of A001859. Cf. A045944, A000326, A033579, A027599, A049451.
Adjacent sequences: A049447 A049448 A049449 this_sequence A049451 A049452 A049453
Sequence in context: A005962 A120548 A120845 this_sequence A092906 A130016 A120550
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Joe Keane (jgk(AT)jgk.org).
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