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A049452
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Pentagonal numbers with even index.
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20
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
Sequence found by reading the line (one of the diagonal axes) from 0, in the direction 0, 5,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = n*(6*n-1).
G.f.: 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)-7. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
a(n) = 4*A000217(n)+A001107(n). - Bruno Berselli, Feb 11 2011
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MAPLE
| [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
| 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
| Cf. A000326, A033570, A049453.
Cf. index to sequences with numbers of the form n*(d*n+10-d)/2 in A140090.
Cf. A001318, A033568. - Omar E. Pol, Sep 08 2011
Cf. A185019.
Sequence in context: A184724 A082005 A099078 * A033445 A050533 A064836
Adjacent sequences: A049449 A049450 A049451 * A049453 A049454 A049455
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org).
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