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Search: id:A014635
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| 0, 6, 28, 66, 120, 190, 276, 378, 496, 630, 780, 946, 1128, 1326, 1540, 1770, 2016, 2278, 2556, 2850, 3160, 3486, 3828, 4186, 4560, 4950, 5356, 5778, 6216, 6670, 7140, 7626, 8128, 8646, 9180, 9730, 10296, 10878, 11476, 12090, 12720, 13366, 14028, 14706
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Even hexagonal numbers.
Number of edges in the join of two complete graphs of order 3n and n, K_3n * K_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
Bisection of A000384. Also, this sequence arises from reading the line from 0, in the direction 0, 6,..., in the square spiral whose vertices are the triangular numbers A000217. Perfect numbers are members of this sequence because a(A134708(n))=A000396(n). Also, positive members are a bisection of A139596. - Omar E. Pol (info(AT)polprimos.com), May 07 2008
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LINKS
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O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
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a(n)=C(4*n,2),n>=0 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
O.g.f.: 2x(3+5x)/(1-x)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2008
a(n)=8n^2-2n. - Omar E. Pol (info(AT)polprimos.com), May 07 2008
a(n)=16*n+a(n-1)-26 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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EXAMPLE
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For n=2, a(2)=16*2+0-26=6; n=3, a(3)=16*3+6-26=28; n=4, a(4)=16*4+28-26=66 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2009]
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MAPLE
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[seq(binomial(4*n, 2), n=0..43)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2007
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 7!, 16}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
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Cf. A000217, A000384, A000396, A134708, A139596.
Sequence in context: A091307 A058007 A033588 this_sequence A034955 A117978 A119174
Adjacent sequences: A014632 A014633 A014634 this_sequence A014636 A014637 A014638
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KEYWORD
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nonn,easy,new
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AUTHOR
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Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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