|
| |
|
|
A008514
|
|
4-dimensional centered cube numbers.
|
|
5
|
|
|
|
1, 17, 97, 337, 881, 1921, 3697, 6497, 10657, 16561, 24641, 35377, 49297, 66977, 89041, 116161, 149057, 188497, 235297, 290321, 354481, 428737, 514097, 611617, 722401, 847601, 988417, 1146097
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Summation of n^4 taken two at a time. - Al Hakanson (hawkuu(AT)gmail.com), May 27 2009
The primes in this sequence are given by A152913. - Jonathan Vos Post, Aug 17 2011
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
|
|
|
FORMULA
|
a(n) = 2*n^4 + 4*n^3 + 6*n^2 + 4*n + 1. - Al Hakanson (hawkuu(AT)gmail.com), May 27 2009, corrected R. J. Mathar, May 29 2009
G.f.:-(x^2+10*x+1)*(x+1)^2/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 09 2009
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), with a(0) = 1, a(1) = 17, a(2) = 97, a(3) = 337, a(4) = 881. - Harvey P. Dale, Jan 28 2013
a(n) = 4*(n+n^2) + 2*(n+n^2)^2 + 1. - Avi Friedlich, Mar 31 2015
a(n) = 2*A002061(n+1)^2 - 1. - Bruce J. Nicholson, Apr 14 2017
|
|
|
MAPLE
|
n^4+(n+1)^4;
|
|
|
MATHEMATICA
|
Total/@Partition[Range[0, 30]^4, 2, 1] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 17, 97, 337, 881}, 30] (* Harvey P. Dale, Jan 28 2013 *)
|
|
|
PROG
|
(Sage) [i^4+(i+1)^4 for i in xrange(0, 36)] # Zerinvary Lajos, Jul 03 2008
(MAGMA) [(n+1)^4+n^4: n in [0..30]]; // Vincenzo Librandi, Aug 27 2011
|
|
|
CROSSREFS
|
Cf. A002061, A152913.
Sequence in context: A078902 A103766 A165347 * A152913 A184327 A262207
Adjacent sequences: A008511 A008512 A008513 * A008515 A008516 A008517
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
