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A168388
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First number in the n-th row of A172002.
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4
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1, 3, 5, 13, 21, 39, 57, 89, 121, 171, 221, 293, 365, 463, 561, 689, 817, 979, 1141, 1341, 1541, 1783, 2025, 2313, 2601, 2939, 3277, 3669, 4061, 4511, 4961, 5473, 5985, 6563, 7141, 7789, 8437, 9159, 9881, 10681, 11481, 12363, 13245, 14213, 15181, 16239, 17297
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6).
G.f.: x*(1 - x^2 + 2*x)*(1 - x + x^2 + x^3)/( (1+x)^2 * (x-1)^4).
a(n) = (12 + n + 3*(-1)^n*n + 2*n^3)/12.
E.g.f.: (1/12)*( -3*x - 12*exp(x) + (12 + 3*x + 6*x^2 + 2*x^3)*exp(2*x) )*exp(-x). (End)
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MATHEMATICA
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LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 3, 5, 13, 21, 39}, 50] (* Harvey P. Dale, Nov 29 2014 *)
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PROG
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(Magma) [(12+n+3*(-1)^n*n+2*n^3)/12: n in [1..60]]; // Vincenzo Librandi, Jul 20 2016
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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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