|
|
A188626
|
|
a(n) = n + (n-1)*2^(n-2).
|
|
3
|
|
|
1, 3, 7, 16, 37, 86, 199, 456, 1033, 2314, 5131, 11276, 24589, 53262, 114703, 245776, 524305, 1114130, 2359315, 4980756, 10485781, 22020118, 46137367, 96469016, 201326617, 419430426, 872415259, 1811939356, 3758096413
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Number of idempotent elements in IDT_n (Identity Difference Full Transformation Semigroup), denoted by E(IDT_n).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n + (n-1)*2^(n-2).
G.f. x*(1-3*x+2*x^2+x^3) / ( (2*x-1)^2*(x-1)^2 ). - R. J. Mathar, Apr 14 2011
E.g.f.: (2*exp(2*x)*x + 4*exp(x)*x - exp(2*x) + 1)/4. - Stefano Spezia, Dec 23 2021
|
|
EXAMPLE
|
For n = 4, #E(IDT_n)= 16.
|
|
MATHEMATICA
|
Table[n + (n-1)*2^(n-2), {n, 1, 50}] (* G. C. Greubel, Nov 01 2018 *)
LinearRecurrence[{6, -13, 12, -4}, {1, 3, 7, 16}, 40] (* Harvey P. Dale, Dec 31 2018 *)
|
|
PROG
|
(Magma) [n + (n-1)*2^(n-2): n in [1..50]]; // G. C. Greubel, Nov 01 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|