A188626 a(n) = n + (n-1)*2^(n-2).

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

Offset: 1

Author

Adeniji, Adenike & Makanjuola, Samuel, Apr 14 2011

Keywords

• nonn
• easy

Comments

Number of idempotent elements in IDT_n (Identity Difference Full Transformation Semigroup), denoted by E(IDT_n).

Examples

			For n = 4, #E(IDT_n)= 16.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Programs

Magma

[n + (n-1)*2^(n-2): n in [1..50]]; // G. C. Greubel, Nov 01 2018

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 *)

PARI

a(n) = n+(n-1)*2^(n-2) \\ Michel Marcus, Jun 29 2013

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