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A016826
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a(n) = (4n + 2)^2.
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13
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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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FORMULA
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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
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)
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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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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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