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A140065
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a(n) = (7*n^2 - 17*n + 12)/2.
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1
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1, 3, 12, 28, 51, 81, 118, 162, 213, 271, 336, 408, 487, 573, 666, 766, 873, 987, 1108, 1236, 1371, 1513, 1662, 1818, 1981, 2151, 2328, 2512, 2703, 2901, 3106, 3318, 3537, 3763, 3996, 4236, 4483, 4737, 4998, 5266, 5541, 5823, 6112, 6408, 6711, 7021, 7338
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OFFSET
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1,2
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COMMENTS
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Binomial transform of [1, 2, 7, 0, 0, 0, ...].
This sequence and 1, 6, 18, 37, 63, 96, ... with signature (3,-3,1) [not yet in OEIS] together contain all numbers k, so that 56*k - 47 is a square. - Klaus Purath, Oct 21 2021
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 4. - Klaus Purath, Oct 21 2021
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EXAMPLE
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a(4) = 28 = (1, 3, 3, 1) * (1, 2, 7, 0) = (1 + 6 + 21 + 0).
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MAPLE
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MATHEMATICA
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Table[(7 n^2 - 17 n + 12)/2, {n, 1, 50}] (* Bruno Berselli, Mar 12 2015 *)
LinearRecurrence[{3, -3, 1}, {1, 3, 12}, 50] (* Harvey P. Dale, May 28 2017 *)
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PROG
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(PARI) x = 'x + O('x^50); Vec(x*(1+6*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 23 2017
(Magma) [(7*n^2 - 17*n + 12)/2 : n in [1..60]]; // Wesley Ivan Hurt, Oct 10 2021
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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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