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A056109
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Fifth spoke of a hexagonal spiral.
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50
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1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321, 386, 457, 534, 617, 706, 801, 902, 1009, 1122, 1241, 1366, 1497, 1634, 1777, 1926, 2081, 2242, 2409, 2582, 2761, 2946, 3137, 3334, 3537, 3746, 3961, 4182, 4409, 4642, 4881, 5126, 5377, 5634, 5897, 6166, 6441
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1+3*x+2*x^2)/(1-3*x+3*x^2-x^3). - Colin Barker, Jan 04 2012
G.f.: (1 + x) * (1 + 2*x) / (1 - x)^3. - Michael Somos, Feb 04 2012
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MAPLE
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seq(coeff(series(factorial(n)*(exp(x)*(3*x^2+5*x+1)), x, n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Oct 07 2018
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MATHEMATICA
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CoefficientList[Series[E^x (1 + 5 x + 3 x^2) , {x, 0, 20}], x]*Table[k!, {k, 0, 100}] (* Stefano Spezia, Oct 06 2018 *)
LinearRecurrence[{3, -3, 1}, {1, 6, 17}, 60] (* Harvey P. Dale, Mar 28 2019 *)
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PROG
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(PARI) {a(n) = 3*n^2 + 2*n + 1}; /* Michael Somos, Aug 03 2006 */
(PARI) Vec((1+3*x+2*x^2)/(1-3*x+3*x^2-x^3)+O(x^100)) \\ Stefano Spezia, Oct 17 2018
(Python) for n in range(0, 100): print(int(3*n**2 + 2*n + 1), end=', ') # Stefano Spezia, Oct 16 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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