|
|
A121671
|
|
Real part of (1 + n*i)^5.
|
|
2
|
|
|
1, -4, 41, 316, 1121, 2876, 6121, 11516, 19841, 31996, 49001, 71996, 102241, 141116, 190121, 250876, 325121, 414716, 521641, 647996, 796001, 967996, 1166441, 1393916, 1653121, 1946876, 2278121, 2649916, 3065441, 3527996, 4041001, 4607996, 5232641, 5918716
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The imaginary term considered as an unsigned real integer = A121672(n). The companion sequence A121672 uses the operation (n + i)^5.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-9*x+71*x^2+61*x^3-4*x^4)/(1-x)^5. - Bruno Berselli, Mar 01 2012
a(n) = (1+n^2)^(5/2)*cos(5*arctan(n)). - Gerry Martens, Apr 06 2024
|
|
EXAMPLE
|
a(4) = 1121 since (1 + 4i)^5 = (1121 + 404i) where 404 = A121672(4).
|
|
MATHEMATICA
|
Table[Re[(1 + n*I)^5], {n, 0, 35}] (* T. D. Noe, Mar 01 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, -4, 41, 316, 1121}, 40] (* Harvey P. Dale, Apr 21 2019 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected and extended by T. D. Noe, Mar 01 2012
|
|
STATUS
|
approved
|
|
|
|