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A081266
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Staggered diagonal of triangular spiral in A051682.
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13
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0, 6, 21, 45, 78, 120, 171, 231, 300, 378, 465, 561, 666, 780, 903, 1035, 1176, 1326, 1485, 1653, 1830, 2016, 2211, 2415, 2628, 2850, 3081, 3321, 3570, 3828, 4095, 4371, 4656, 4950, 5253, 5565, 5886, 6216, 6555, 6903, 7260, 7626, 8001, 8385, 8778, 9180
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Staggered diagonal of triangular spiral in A051682, between (0,4,17) spoke and (0,7,23) spoke
If Y is a fixed 3-subset of a (3n+1)-set X then a(n) is the number of (3n-1)-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Oct 28 2007
a(n) = A000217(3*n); a(2*n) = A144314(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2008]
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LINKS
| Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n) = 6C(n, 1)+9C(n, 2). Binomial transform of (0, 6, 9, 0, 0, 0, ...). a(n)=3n(3n+1)/2. G.f.: (6x+3x^2)/(1-x)^3.
a(n)=3*A005449(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 27 2009]
a(n)=9*n+a(n-1)-3 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=9*1+0-3=6; a(2)=9*2+6-3=21; a(3)=9*3+21-3=45 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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MAPLE
| seq(binomial(3*n+1, 2), n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 21 2007
a:=n->sum(j, j=0..n): seq(a(3*n), n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 9}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
| Cf. A022266, A062725.
A014105, A033585, A144312. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2008]
Sequence in context: A048036 A119868 A175729 * A087863 A051941 A163715
Adjacent sequences: A081263 A081264 A081265 * A081267 A081268 A081269
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
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