login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134594 a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5. 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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

(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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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]

G.f.: (1+x)*(5-4*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007

a(n) = 2*n + a(n-1) + 9 (with a(0)=5). - Vincenzo Librandi, Nov 23 2010

E.g.f.: (5 +11*x +x^2)*exp(x). - G. C. Greubel, Nov 23 2018

MATHEMATICA

Table[(n^2 + 10n + 5), {n, 0, 50}]

LinearRecurrence[{3, -3, 1}, {5, 16, 29}, 50] (* G. C. Greubel, Nov 23 2018 *)

PROG

(PARI) a(n)=n^2+10*n+5 \\ Charles R Greathouse IV, Jun 17 2017

(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

(GAP) List([0..50], n->n^2+10*n+5); # Muniru A Asiru, Nov 24 2018

CROSSREFS

Cf. A134593.

Sequence in context: A063290 A299882 A212457 * A222535 A063076 A270805

Adjacent sequences:  A134591 A134592 A134593 * A134595 A134596 A134597

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Nov 04 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 17:17 EST 2019. Contains 329970 sequences. (Running on oeis4.)