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Search: id:A049452
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| A049452 |
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Pentagonal numbers with even index. |
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+0
13
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| 0, 5, 22, 51, 92, 145, 210, 287, 376, 477, 590, 715, 852, 1001, 1162, 1335, 1520, 1717, 1926, 2147, 2380, 2625, 2882, 3151, 3432, 3725, 4030, 4347, 4676, 5017, 5370, 5735, 6112, 6501, 6902, 7315, 7740, 8177, 8626, 9087, 9560, 10045, 10542
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If Y is a 3-subset of an (2n+1)-set X then, for n>=4, a(n-1) is the number of 4-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 16 2007
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FORMULA
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a(n) = n*(6*n-1).
G.f.: A(x) = x*(5+7*x)/(1-x)^3.
a(n)=C(6*n,2)/3,n>=0 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
a(n)=A001105(n)+A033991(n) =A033428(n)+A049450(n) = A022266(n)+A000326(n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
a(n)=12*n+a(n-1)-19 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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For n=2, a(2)=12*2+0-19=5; n=3, a(3)=12*3+5-19=22; n=4, a(4)=12*4+22-19=51 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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MAPLE
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[seq(binomial(6*n, 2)/3, n=0..42)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
seq(n*(6*n-1), n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +5; AppendTo[lst, s], {n, 0, 7!, 12}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
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Cf. A000326, A033570, A049453.
Sequence in context: A085101 A082005 A099078 this_sequence A033445 A050533 A064836
Adjacent sequences: A049449 A049450 A049451 this_sequence A049453 A049454 A049455
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KEYWORD
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nonn,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org).
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