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A184750
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a(n) = largest k such that A000326(n+1) = A000326(n) + (A000326(n) mod k), or 0 if no such k exists.
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3
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0, 0, 0, 0, 19, 32, 48, 67, 89, 114, 142, 173, 207, 244, 284, 327, 373, 422, 474, 529, 587, 648, 712, 779, 849, 922, 998, 1077, 1159, 1244, 1332, 1423, 1517, 1614, 1714, 1817, 1923, 2032, 2144, 2259, 2377, 2498, 2622, 2749
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OFFSET
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1,5
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COMMENTS
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LINKS
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FORMULA
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a(n) = (3n^2-7n-2)/2 for n >= 5 and a(n) = 0 for n <= 4.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>7. G.f.: x^5*(9*x^2-25*x+19) / (1-x)^3. - Colin Barker, Apr 05 2014
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EXAMPLE
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For n = 3 we have A000326(3) = 12, A000326(4) = 22; there is no k such that 22 - 12 = 10 = (12 mod k), hence a(3) = 0.
For n = 5 we have A000326(5) = 35, A000326(6) = 51; 19 is the largest k such that 51 - 35 = 16 = (35 mod k), hence a(5) = 19; a(5) = (75-35-2)/2 = 19.
For n = 25 we have A000326(25) = 925, A000326(26) = 1001; 849 is the largest k such that 1001 - 925 = 76 = (925 mod k), hence a(25) = 849; a(25) = (1875-175-2)/2 = 849.
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MAPLE
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MATHEMATICA
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Table[(3 n^2 - 7 n - 2) Sign[Floor[n/5]]/2, {n, 50}] (* Wesley Ivan Hurt, Apr 05 2014 *)
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PROG
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(PARI) concat([0, 0, 0, 0], Vec(-x^5*(9*x^2-25*x+19)/(x-1)^3 + O(x^100))) \\ Colin Barker, Apr 05 2014
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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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EXTENSIONS
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STATUS
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approved
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