Search: a169914 -id:a169914
|
| |
|
|
A169912
|
|
Number of irreducible Boolean polynomials of degree n.
|
|
+10
8
|
|
|
|
1, 2, 1, 3, 5, 9, 19, 39, 77, 168, 323, 682, 1424, 2902, 5956, 12368, 25329, 51866, 106427, 217216, 442313, 902921, 1833029, 3719745, 7548521, 15264350, 30859444, 62355854, 125773168, 253461052, 510471015, 1027067090, 2065390101, 4151081457, 8336751732, 16734781946, 33583213577, 67357328359, 135056786787
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Let B be the Boolean ring {0,1} with 0+0=0, 0+1=1+1=1, 0*0=0*1=0, 1*1=1 (0 = FALSE, 1 = TRUE, + = OR, * = AND); then a(n) = number of irreducible elements of degree n in the polynomial ring B[X].
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
a(0) = 1: 1.
a(1) = 2: X and X+1.
a(2) = 1: X^2+1 (note that X^2+X+1 = (X+1)^2 is reducible).
a(3) = 3: X^3+1, X^3+X+1, X^3+X^2+1.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A169913
|
|
Number of reducible Boolean polynomials of degree n.
|
|
+10
2
|
|
|
|
0, 0, 3, 5, 11, 23, 45, 89, 179, 344, 701, 1366, 2672, 5290, 10428, 20400, 40207, 79206, 155717, 307072, 606263, 1194231, 2361275, 4668863, 9228695, 18290082, 36249420, 71861874, 142662288, 283409860, 563270809, 1120416558, 2229577195, 4438853135, 8843117452, 17624956422, 35136263159, 70081625113, 139821120157
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.005 seconds
|
