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A227316
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a(n) = n(n+1) if n == 0 or 1 (mod 4), otherwise a(n) = n(n+1)/2.
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3
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0, 2, 3, 6, 20, 30, 21, 28, 72, 90, 55, 66, 156, 182, 105, 120, 272, 306, 171, 190, 420, 462, 253, 276, 600, 650, 351, 378, 812, 870, 465, 496, 1056, 1122, 595, 630, 1332, 1406, 741, 780, 1640, 1722, 903, 946, 1980, 2070, 1081, 1128
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3*a(n-1) -6*a(n-2) +10*a(n-3) -12*a(n-4) +12*a(n-5) -10*(n-6) +6*(n-7) -3*a(n-8) +a(n-9) = 3*a(n-4) -3*a(n-8) +a(n-12).
G.f.: x*(2-3*x+9*x^2+3*x^5+x^6)/((1-x)^3*(1+x^2)^3). - Bruno Berselli, Jul 10 2013
Sum_{n>=1} 1/a(n) = 1 + log(2)/2. - Amiram Eldar, Aug 12 2022
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EXAMPLE
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a(0) = 2*0 = 0, a(1) = 2*1 = 2, a(2) = 1*3 = 3, a(3) = 1*6 = 6, a(4) = 2*10 = 20.
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MATHEMATICA
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a[n_] := n*(n+1)/4*GCD[n-1, 4]*GCD[n, 4]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 10 2013 *)
Table[If[Mod[n, 4]<2, n(n+1), (n(n+1))/2], {n, 0, 50}] (* or *) LinearRecurrence[ {3, -6, 10, -12, 12, -10, 6, -3, 1}, {0, 2, 3, 6, 20, 30, 21, 28, 72}, 50] (* Harvey P. Dale, Aug 26 2016 *)
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PROG
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(Magma) [(3+(-1)^Floor(n/2))*n*(n+1)/4: n in [0..50]]; // Bruno Berselli, Jul 10 2013
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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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