

A134593


a(n) = 5*n^2 + 10*n + 1. Coefficients of the rational part of (1 + sqrt(n))^5.


4



1, 16, 41, 76, 121, 176, 241, 316, 401, 496, 601, 716, 841, 976, 1121, 1276, 1441, 1616, 1801, 1996, 2201, 2416, 2641, 2876, 3121, 3376, 3641, 3916, 4201, 4496, 4801, 5116, 5441, 5776, 6121, 6476, 6841, 7216, 7601, 7996, 8401, 8816, 9241, 9676, 10121
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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

Table of n, a(n) for n=0..44.
D. E. Knuth, Donald Knuth's 24th Annual Christmas Lecture: Dancing Links, Stanfordonline, Video published on YouTube, Dec 12, 2018.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 5*n^2 + 10*n + 1.
G.f.: (4*x^2  13*x  1)/(x1)^3.  R. J. Mathar, Nov 14 2007
a(n) = a(n1) + 10*n + 5 (with a(0)=1).  Vincenzo Librandi, Nov 23 2010


MATHEMATICA

Table[(5n^2 + 10n + 1), {n, 0, 50}]


PROG

(Python)
...for i in range(1, 1000):
.......print(5*i**24)
# Ruskin Harding, Mar 27 2013
(PARI) a(n)=5*n^2+10*n+1 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A134593.
Sequence in context: A044093 A044474 A188861 * A227816 A200408 A280184
Adjacent sequences: A134590 A134591 A134592 * A134594 A134595 A134596


KEYWORD

nonn,easy


AUTHOR

Artur Jasinski, Nov 04 2007


EXTENSIONS

Edited by Charles R Greathouse IV, Aug 09 2010


STATUS

approved



