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A120328
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n^2+(n+1)^2+(n+2)^2.
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0
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2, 5, 14, 29, 50, 77, 110, 149, 194, 245, 302, 365, 434, 509, 590, 677, 770, 869, 974, 1085, 1202, 1325, 1454, 1589, 1730, 1877, 2030, 2189, 2354, 2525, 2702, 2885, 3074, 3269, 3470, 3677, 3890, 4109, 4334, 4565, 4802, 5045, 5294, 5549, 5810, 6077, 6350
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,1
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COMMENTS
| A rectangular prism with sides n, n+1, and n+2 will have four diagonals of different lengths. The sum of the squares of all four is three times the numbers in this sequence beginning with 14 (n=3 in the sequence). [J. M. Bergot, Sep 15 2011]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=A005918(n+1), n>=0. O.g.f.: (2-x+5x^2)/(x(1-x)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008]
a(n)=3*(2*n+1)+a(n-1) (with a(-1)=2) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2010]
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MAPLE
| [seq (n^2+(n+1)^2+(n+2)^2, n=-1..45)];
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MATHEMATICA
| lst={}; Do[a=(n^2+(n+1)^2+(n+2)^2); AppendTo[lst, a], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 25 2009]
Table[Total[Range[n, n+2]^2], {n, -1, 45}] [From Harvey P. Dale, Jan. 23, 2011]
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PROG
| sage: [i^2+(i+1)^2+(i+2)^2 for i in xrange(-1, 46)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
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CROSSREFS
| Cf. A027602.
Sequence in context: A022630 A047133 A031874 * A026011 A022913 A056358
Adjacent sequences: A120325 A120326 A120327 * A120329 A120330 A120331
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KEYWORD
| easy,nonn
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AUTHOR
| Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 21 2006
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