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A134594
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a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5.
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2
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5, 16, 29, 44, 61, 80, 101, 124, 149, 176, 205, 236, 269, 304, 341, 380, 421, 464, 509, 556, 605, 656, 709, 764, 821, 880, 941, 1004, 1069, 1136, 1205, 1276, 1349, 1424, 1501, 1580, 1661, 1744, 1829, 1916, 2005, 2096, 2189, 2284, 2381, 2480, 2581, 2684
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OFFSET
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0,1
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COMMENTS
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(1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). For coefficients of the rational part see A134593.
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LINKS
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FORMULA
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a(n) = ((1+sqrt(n))^5 - (5*n^2 + 10*n + 1))/sqrt(n), for n > 0. [corrected by Jon E. Schoenfield, Nov 23 2018]
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MATHEMATICA
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Table[(n^2 + 10n + 5), {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {5, 16, 29}, 50] (* G. C. Greubel, Nov 23 2018 *)
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PROG
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(Magma) [n^2 +10*n +5: n in [0..50]]; // G. C. Greubel, Nov 23 2018
(Sage) [n^2 +10*n +5 for n in range(50)] # G. C. Greubel, Nov 23 2018
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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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