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A016802
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a(n) = (4*n)^2.
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21
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0, 16, 64, 144, 256, 400, 576, 784, 1024, 1296, 1600, 1936, 2304, 2704, 3136, 3600, 4096, 4624, 5184, 5776, 6400, 7056, 7744, 8464, 9216, 10000, 10816, 11664, 12544, 13456, 14400, 15376, 16384, 17424, 18496, 19600, 20736, 21904, 23104, 24336, 25600, 26896
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OFFSET
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0,2
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COMMENTS
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A bisection of A016742. Sequence arises from reading the line from 0, in the direction 0, 16, ... in the square spiral whose vertices are the squares A000290. - Omar E. Pol, May 24 2008
Also, sequence found by reading the line from 0, in the direction 0, 16, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Sep 10 2011
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 16*n^2 = A000290(n)*16. - Omar E. Pol, Dec 11 2008
a(n) = A001105(n)*8 = A016742(n)*4 = A139098(n)*2. - Omar E. Pol, Dec 13 2008
a(n) = a(n-1) + 16*(2*n-1) (with a(0)=0). - Vincenzo Librandi, Nov 20 2010
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/96.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/192.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/4)/(Pi/4).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/4)/(Pi/4) = 2*sqrt(2)/Pi (A112628). (End)
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PROG
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(PARI) a(n) = (4*n)^2; \\ Michel Marcus, Mar 04 2014
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CROSSREFS
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Cf. A000290, A001539, A016742, A016754, A016814, A016826, A016838, A001105, A112628, A139098.
Sequence in context: A316301 A072128 A277016 * A309573 A205064 A102860
Adjacent sequences: A016799 A016800 A016801 * A016803 A016804 A016805
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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