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A016790
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a(n) = (3n+2)^2.
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17
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1, 4, 25, 64, 121, 196, 289, 400, 529, 676, 841, 1024, 1225, 1444, 1681, 1936, 2209, 2500, 2809, 3136, 3481, 3844, 4225, 4624, 5041, 5476, 5929, 6400, 6889, 7396, 7921, 8464, 9025, 9604, 10201, 10816, 11449, 12100, 12769, 13456, 14161, 14884, 15625, 16384
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OFFSET
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-1,2
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COMMENTS
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If Y is a fixed 2-subset of a (3n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - _Milan Janjic_, Oct 21 2007
The digit root of the sequence, i.e., A010888(a(n)) for n>=0, is a repeating pattern of {4,7,1}, cf. A100402. - _Ram Shankar_, Apr 14 2015
With a different offset, partial sums of A298035. - _N. J. A. Sloane_, Jan 22 2018
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LINKS
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FORMULA
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a(n) = A016958(n)/4. - _Zerinvary Lajos_, Jun 30 2009
From _Wesley Ivan Hurt_, Apr 14 2015: (Start)
G.f.: (4+13*x+x^2)/(1-x)^3.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). (End)
a(n) = a(n-1)+3*(6*n+1). - _Miquel Cerda_, Oct 25 2016
Sum_{n>=0} 1/a(n) = A294967. - _Amiram Eldar_, Nov 12 2020
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MAPLE
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A016790:=n->(3*n+2)^2: seq(A016790(n), n=0..50); # _Wesley Ivan Hurt_, Apr 14 2015
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MATHEMATICA
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(3 Range[0, 50] + 2)^2 (* _Wesley Ivan Hurt_, Apr 14 2015 *)
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PROG
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(Magma) [(3*n+2)^2: n in [0..50]]; // _Vincenzo Librandi_, May 06 2011
(PARI) vector(50, n, n--; (3*n+2)^2) \\ _Derek Orr_, Apr 14 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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_N. J. A. Sloane_
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EXTENSIONS
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Notation in formula cleaned up by _R. J. Mathar_, Aug 05 2010
Added a(-1)=1 and fixed b-file. Note: this sequence should really be changed to a(n) = (3n-1)^2 and have offset 0. - _N. J. A. Sloane_, Jan 22 2018
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STATUS
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approved
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