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A016826
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a(n) = (4n + 2)^2.
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10
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4, 36, 100, 196, 324, 484, 676, 900, 1156, 1444, 1764, 2116, 2500, 2916, 3364, 3844, 4356, 4900, 5476, 6084, 6724, 7396, 8100, 8836, 9604, 10404, 11236, 12100, 12996, 13924, 14884, 15876, 16900, 17956
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OFFSET
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0,1
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COMMENTS
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A bisection of A016742. Sequence arises from reading the line from 4, in the direction 4, 36, ... in the square spiral whose vertices are the squares A000290. - Omar E. Pol, May 24 2008
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = a(n-1) + 32*n (with a(0)=4). - Vincenzo Librandi, Dec 15 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), with a(0)=4, a(1)=36, a(2)=100. - Harvey P. Dale, Nov 24 2011
G.f.: -((4*(x^2+6*x+1))/(x-1)^3). - Harvey P. Dale, Nov 24 2011
a(n) = A000290(A016825(n)). - Wesley Ivan Hurt, Feb 24 2014
From Amiram Eldar, Jun 28 2020: (Start)
Sum_{n>=0} 1/a(n) = Pi^2/32.
Sum_{n>=0} (-1)^n/a(n) = G/4, where G is the Catalan constant (A006752). (End)
From Amiram Eldar, Jan 29 2021: (Start)
Product_{n>=0} (1 + 1/a(n)) = cosh(Pi/4).
Product_{n>=0} (1 - 1/a(n)) = 1/sqrt(2) (A010503). (End)
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MAPLE
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A016826:=n->(4*n + 2)^2; seq(A016826(n), n=0..40); # Wesley Ivan Hurt, Feb 24 2014
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MATHEMATICA
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(4*Range[0, 40]+2)^2 (* or *) LinearRecurrence[{3, -3, 1}, {4, 36, 100}, 40] (* Harvey P. Dale, Nov 24 2011 *)
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PROG
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(PARI) a(n)=(4*n+2)^2 \\ Charles R Greathouse IV, Oct 07 2015
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CROSSREFS
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Equals A001539 + 1.
Cf. A000290, A010503, A016742, A016754, A016802, A016814, A016838.
Sequence in context: A193833 A193183 A152760 * A190318 A193874 A254939
Adjacent sequences: A016823 A016824 A016825 * A016827 A016828 A016829
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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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STATUS
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approved
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