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%I #55 Nov 12 2020 10:34:32
%S 1,16,49,100,169,256,361,484,625,784,961,1156,1369,1600,1849,2116,
%T 2401,2704,3025,3364,3721,4096,4489,4900,5329,5776,6241,6724,7225,
%U 7744,8281,8836,9409,10000,10609,11236
%N a(n) = (3*n+1)^2.
%C From _Paul Curtz_, Mar 28 2019: (Start)
%C Sequence is a spoke of the hexagonal spiral built from the terms of A016777:
%C .
%C \
%C 100--97--94--91
%C \ \
%C 49--46--43 88
%C / \ \ \
%C 52 16--13 40 85
%C / / \ \ \ \
%C 55 19 1 10 37 82
%C / / / / / /
%C 58 22 4---7 34 79
%C \ \ / /
%C 61 25--28--31 76
%C \ /
%C 64--67--70--73
%C (End)
%H Shawn A. Broyles, <a href="/A016778/b016778.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + 3*(6*n-1); a(0)=1. - _Vincenzo Librandi_, Nov 20 2010
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=16, a(2)=49. - _Harvey P. Dale_, Mar 03 2013
%F a(n) = A247792(n) + 6*n. - _Miquel Cerda_, Oct 23 2016
%F G.f.: (1 + 13*x + 4*x^2)/(1 - x)^3. - _Ilya Gutkovskiy_, Oct 23 2016
%F a(n) = A000212(3*n) + A000212(1+3*n) + A000212(2+3*n). - _Paul Curtz_, Mar 28 2019
%F From _Amiram Eldar_, Nov 12 2020: (Start)
%F Sum_{n>=0} 1/a(n) = A214550.
%F Sum_{n>=0} (-1)^n/a(n) = A262178. (End)
%t (3*Range[0,50]+1)^2 (* or *) LinearRecurrence[{3,-3,1},{1,16,49},50] (* _Harvey P. Dale_, Mar 03 2013 *)
%o (Maxima) A016778(n):=(3*n+1)^2$
%o makelist(A016778(n),n,0,20); /* _Martin Ettl_, Nov 12 2012 */
%o (PARI) a(n)=(3*n+1)^2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A016777, A016779, A016780, A016781, A214550.
%Y Cf. A000212, A214550, A262178.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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