|
Search: id:A134594
|
|
|
| A134594 |
|
a(n)=n^2 + 10n + 5 : coefficients of irrrational part of (1+Sqrt[n])^5. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
(1+Sqrt[n])^5=(5n^2 + 10n + 1) + (n^2 + 10n + 5)Sqrt[n]. For coefficients by rational part see A134593.
|
|
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)+7 (with a(1)=5) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
|
|
EXAMPLE
|
For n=2, a(2)=2*2+5+7=16; n=3, a(3)=2*3+16+7=29; n=4, a(4)=2*4+29+7=44 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
|
|
MATHEMATICA
|
Table[(n^2 + 10n + 5), {n, 0, 50}]
|
|
CROSSREFS
|
Cf. A134593.
Sequence in context: A063135 A030573 A063290 this_sequence A063076 A132479 A045944
Adjacent sequences: A134591 A134592 A134593 this_sequence A134595 A134596 A134597
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Artur Jasinski (grafix(AT)csl.pl), Nov 04 2007
|
|
|
Search completed in 0.003 seconds
|
