OFFSET
0,2
COMMENTS
(1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). Coefficients of the irrational part are A134594.
Number of entries required to describe the options and constraints in Don Knuth's formulation of the n nonattacking queens on an n X n board problem (A000170) as input for his DLX (Dancing Links eXact coverage) program. Can be seen as "entries successfully read" in the video from his 2018 Annual Christmas Lecture. - Hugo Pfoertner, Jan 09 2019
LINKS
D. E. Knuth, Donald Knuth's 24th Annual Christmas Lecture: Dancing Links, Stanfordonline, Video published on YouTube, Dec 12, 2018.
Takao Komatsu, Ritika Goel, and Neha Gupta, The Frobenius number for the triple of the 2-step star numbers, arXiv:2409.14788 [math.CO], 2024. See p. 2.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (4*x^2 - 13*x - 1)/(x-1)^3. - R. J. Mathar, Nov 14 2007
a(n) = a(n-1) + 10*n + 5 (with a(0)=1). - Vincenzo Librandi, Nov 23 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Wesley Ivan Hurt, May 17 2021
E.g.f.: exp(x)*(1 + 15*x + 5*x^2). - Stefano Spezia, Sep 27 2024
MATHEMATICA
Table[(5n^2 + 10n + 1), {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {1, 16, 41}, 50] (* Harvey P. Dale, Oct 20 2023 *)
PROG
(Python)
print([5*i**2-4 for i in range(1, 100)])
# Ruskin Harding, Mar 27 2013
(PARI) a(n)=5*n^2+10*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Nov 04 2007
EXTENSIONS
Edited by Charles R Greathouse IV, Aug 09 2010
STATUS
approved