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A171182
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Period 6: repeat [0, 1, 1, 1, 0, 2].
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8
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0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1
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OFFSET
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1,6
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COMMENTS
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The number of divisors d of n of the form d=2 or 3. - Vladimir Shevelev, May 21 2010
a(n) = s(n+6), where s(k) is the number of partitions of k into distinct parts such that max(p) = 2 + min(p) for k >= 1, and (s(0)..s(6)) = (0,0,0,0,1,0,2). - Clark Kimberling, Apr 15 2014
Number of r X s integer sided rectangles such that r < s, r + s = 2n, r | s and (s - r)/2 | s. - Wesley Ivan Hurt, Apr 24 2020
Number of positive integer solutions, (r,s,t), of the equation r^2 + t*s^2 = (n + 6)^2, where r + s = n + 6 and t < r <= s. For example, when n=6 we have the two solutions (4,8,2) and (6,6,3) since 4^2 + 2*8^2 = 12^2 and 6^2 + 3*6^2 = 12^2. - Wesley Ivan Hurt, Oct 04 2020
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LINKS
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Table of n, a(n) for n=1..105.
Vladimir Shevelev, A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function sigma_x(n), arXiv:0903.1743 [math.NT], 2009. [From Vladimir Shevelev, May 21 2010]
Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1).
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FORMULA
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a(n) = A115357(n-2) for n>1. - R. J. Mathar, Dec 09 2009
a(n) = (1/18)*{-5*(n mod 6)+4*[(n+1) mod 6]+[(n+2) mod 6]+[(n+3) mod 6]-2*[(n+4) mod 6]+7*[(n+5) mod 6]}. - Paolo P. Lava, Apr 21 2010
a(2)=1,a(3)=1,a(5)=0, otherwise a(n) = a(n-2)+a(n-3)-a(n-5), where we put a(n)=0, if n<0. - Vladimir Shevelev, May 21 2010
a(n) = floor(((n+1) mod 6)/3) + 2*floor(((n+5) mod 6)/5). - Gary Detlefs, Feb 15 2014
From Wesley Ivan Hurt, Aug 27 2014: (Start)
G.f.: (2+2*x+x^2)/(1+x-x^3-x^4).
a(n) + a(n-1) = a(n-3) + a(n-4) for n>4.
a(n) = (1 + floor((n-3)^2/2)) mod 3. (End)
a(n) = (5 + 3*cos(n*Pi) + 4*cos(2*n*Pi/3))/6. - Wesley Ivan Hurt, Jun 19 2016
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MAPLE
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A171182:=n->(1+floor((n-3)^2/2)) mod 3: seq(A171182(n), n=1..100); # Wesley Ivan Hurt, Aug 27 2014
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MATHEMATICA
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PadRight[{}, 110, {0, 1, 1, 1, 0, 2}] (* Harvey P. Dale, Jan 28 2013 *)
LinearRecurrence[{-1, 0, 1, 1}, {0, 1, 1, 1}, 105] (* Ray Chandler, Aug 26 2015 *)
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PROG
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(MAGMA) &cat[[0, 1, 1, 1, 0, 2]^^20]; // Wesley Ivan Hurt, Jun 19 2016
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CROSSREFS
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Cf. A178142. - Vladimir Shevelev, May 21 2010
Cf. A115357.
Sequence in context: A280748 A117454 A115357 * A333806 A063962 A084114
Adjacent sequences: A171179 A171180 A171181 * A171183 A171184 A171185
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KEYWORD
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nonn,easy,less
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AUTHOR
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Juri-Stepan Gerasimov, Dec 04 2009, Dec 07 2009
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EXTENSIONS
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Edited by Charles R Greathouse IV, Mar 23 2010
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STATUS
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approved
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