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A004320
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n*(n+1)*(n+2)^2/6.
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7
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0, 3, 16, 50, 120, 245, 448, 756, 1200, 1815, 2640, 3718, 5096, 6825, 8960, 11560, 14688, 18411, 22800, 27930, 33880, 40733, 48576, 57500, 67600, 78975, 91728, 105966, 121800, 139345, 158720, 180048, 203456, 229075, 257040, 287490, 320568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Consider the set B(n) = {1,2,3,...n}. Let a(0) = 0. Then a(n) = Sum [ b(i)^2 - b(j)^2] for all i, j = 1 to n, b(i) belongs to B(n). E.g. a(3) = (3^2-1^2) + (3^2-2^2) +(2^2-1^2)= 16. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2001
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| G.f.: x*(3+x)/(1-x)^5 - Paul Barry, Feb 27 2003
a(n) = (n+2)*C(n+2,3) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
a(n) = A047929(n)/6 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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MAPLE
| [seq ((n+2)*(binomial(n+2, 3)), n=0..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
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MATHEMATICA
| a[n_]:=(n+(n+1)+(n+2))*(n-1)*n*(n+1)/18; lst={}; Do[AppendTo[lst, a[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky, Oct 08 2009]
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PROG
| (MAGMA) [n*(n+1)*(n+2)^2/6: n in [0..40] ]; // Vincenzo Librandi, Aug 19 2011
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CROSSREFS
| Sequence in context: A092466 A152618 A172482 * A089363 A000574 A041233
Adjacent sequences: A004317 A004318 A004319 * A004321 A004322 A004323
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2006
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