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A168200
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a(n) = 3*n - a(n-1) + 1, with a(1)=4.
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2
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4, 3, 7, 6, 10, 9, 13, 12, 16, 15, 19, 18, 22, 21, 25, 24, 28, 27, 31, 30, 34, 33, 37, 36, 40, 39, 43, 42, 46, 45, 49, 48, 52, 51, 55, 54, 58, 57, 61, 60, 64, 63, 67, 66, 70, 69, 73, 72, 76, 75, 79, 78, 82, 81, 85, 84, 88, 87, 91, 90, 94, 93, 97, 96, 100, 99, 103, 102, 106, 105
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = +1*a(n-1) + 1*a(n-2) - 1*a(n-3).
G.f.: x*(4-x)/(1-x-x^2+x^3) = x*(4-x)/((1+x)*(1-x)^2). (End)
Sum_{n>=1} (-1)^n/a(n) = 1 - Pi/(6*sqrt(3)) - log(3)/2. - Amiram Eldar, Feb 23 2023
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MATHEMATICA
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RecurrenceTable[{a[1]==4, a[n]==3n-a[n-1]+1}, a, {n, 70}] (* or *) LinearRecurrence[{1, 1, -1}, {4, 3, 7}, 80] (* Harvey P. Dale, Jul 31 2014 *)
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PROG
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(Magma) [(6*n+5-5*(-1)^n)/4: n in [1..70]];
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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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