|
| |
| |
|
|
|
1, 2, 257, 6562, 65537, 390626, 1679617, 5764802, 16777217, 43046722, 100000001, 214358882, 429981697, 815730722, 1475789057, 2562890626, 4294967297, 6975757442, 11019960577, 16983563042, 25600000001, 37822859362, 54875873537
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Let Phi_k(x) be the k-th cyclotomic polynomial and form the sequence Phi_k(0), Phi_k(1), Phi_k(2), ... This gives A000027 (k=2), A002061 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), A060891 (k=18), A060892 (k=20), A060893 (k=24), A060894 (k=30), A060895 (k=32), A060896 (k=36).
|
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=0,...,1000
|
|
|
FORMULA
|
a(0)=1, a(1)=2, a(2)=257, a(3)=6562, a(4)=65537, a(5)=390626, a(6)=1679617, a(7)=5764802, a(8)=16777217, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Mar 12 2013
|
|
|
EXAMPLE
|
G.f.: (1-7*x+275*x^2+4237*x^3+15689*x^4+15563*x^5+4321*x^6+239*x^7+2*x^8)/ (1-x)^9. [Colin Barker, Apr 21 2012]
|
|
|
MATHEMATICA
|
Table[n^8+1, {n, 0, 40}] (* From Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 2, 257, 6562, 65537, 390626, 1679617, 5764802, 16777217}, 40] (* Harvey P. Dale, Mar 12 2013 *)
|
|
|
PROG
|
(PARI) { for (n=0, 1000, write("b060890.txt", n, " ", n^8 + 1); ) } [From Harry J. Smith, Jul 14 2009]
|
|
|
CROSSREFS
|
Cf. A002522.
Sequence in context: A190539 A078168 A003380 * A085316 A006686 A100269
Adjacent sequences: A060887 A060888 A060889 * A060891 A060892 A060893
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, May 05 2001
|
|
|
STATUS
|
approved
|
| |
|
|
