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A134594
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n^2 + 10n + 5: coefficients of the irrrational part of (1+sqrt(n))^5.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| (1+sqrt(n))^5 = (5n^2 + 10n + 1) + (n^2 + 10n + 5)sqrt(n). For coefficients of the rational part see A134593.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n)=((1+Sqrt[n])^5-(5n^2 + 10n + 1)Sqrt[n])/Sqrt[n]
G.f.: (1+x)(4x-5)/(x-1)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=2*n+a(n-1)+9 (with a(0)=5) [From Vincenzo Librandi, Nov 23 2010]
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MATHEMATICA
| Table[(n^2 + 10n + 5), {n, 0, 50}]
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CROSSREFS
| Cf. A134593.
Sequence in context: A063135 A030573 A063290 * A063076 A132479 A045944
Adjacent sequences: A134591 A134592 A134593 * A134595 A134596 A134597
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KEYWORD
| nonn,easy
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Nov 04 2007
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