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A143208
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a(1)=2; for n>1, a(n) = (4-9*n+3*n^2)/2.
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1
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2, -1, 2, 8, 17, 29, 44, 62, 83, 107, 134, 164, 197, 233, 272, 314, 359, 407, 458, 512, 569, 629, 692, 758, 827, 899, 974, 1052, 1133, 1217, 1304, 1394, 1487, 1583, 1682, 1784, 1889, 1997, 2108, 2222, 2339, 2459, 2582, 2708, 2837, 2969, 3104, 3242, 3383, 3527, 3674
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OFFSET
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1,1
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COMMENTS
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Old Name was: A sequence based on odd numbers of the type 3*n + 2: a(n) = a(n - 1) + n - 1; A000096; f(n) = 3*a(n)+2.
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LINKS
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FORMULA
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a(n) = (4-9*n+3*n^2)/2 for n>1.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4.
G.f.: x*(3*x^3-11*x^2+7*x-2) / (x-1)^3. (End).
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EXAMPLE
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G.f. = 2*x - x^2 + 2*x^3 + 8*x^4 + 17*x^5 + 29*x^6 + 44*x^7 + 62*x^8 + ...
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MATHEMATICA
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a[0] = 0; a[1] = -1; a[n_] := a[n] = a[n - 1] + n - 1; a1 = Table[a[n], {n, 0, 30}]; f[n_] := 3*a[n] + 2; Table[f[n], {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {2, -1, 2, 8}, 60] (* Harvey P. Dale, Mar 22 2018 *)
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PROG
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(PARI) Vec(x*(3*x^3-11*x^2+7*x-2)/(x-1)^3 + O(x^100)) \\ Colin Barker, Apr 14 2014
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CROSSREFS
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KEYWORD
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sign,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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