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A108195
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a(n) = n^2 + 5*n - 1.
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6
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5, 13, 23, 35, 49, 65, 83, 103, 125, 149, 175, 203, 233, 265, 299, 335, 373, 413, 455, 499, 545, 593, 643, 695, 749, 805, 863, 923, 985, 1049, 1115, 1183, 1253, 1325, 1399, 1475, 1553, 1633, 1715, 1799, 1885, 1973, 2063, 2155, 2249, 2345, 2443, 2543, 2645
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OFFSET
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1,1
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COMMENTS
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a(n-2) = n*(n + 1) - 7, n>=0, with a(-2) = -7, a(-1) = -5 and a(0) = -1, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 29 for b = 2*n + 1. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - Wolfdieter Lang, Aug 16 2013
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LINKS
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FORMULA
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EXAMPLE
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....... +---+ ......... The Cross of Lorraine
....... | + | ......... having n=2 crossbeams
... +---+---+---+ ..... consists of a(2)=13 squares
... | + | + | + |
... +---+---+---+
....... | + |
+---+---+---+---+---+
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+---+---+---+---+---+
....... | + |
....... +---+
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....... +---+
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....... +---+
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MAPLE
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with (combinat):seq(fibonacci(3, n)+n-8, n=3..51); # Zerinvary Lajos, Jun 07 2008
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MATHEMATICA
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CoefficientList[Series[(5 + 3 x - x^2 - 5 x)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 11 2014 *)
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PROG
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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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