A188716 a(n) = n + (n-1)*(2^n-2).

1, 1, 4, 15, 46, 125, 316, 763, 1786, 4089, 9208, 20471, 45046, 98293, 212980, 458739, 983026, 2097137, 4456432, 9437167, 19922926, 41943021, 88080364, 184549355, 385875946, 805306345, 1677721576, 3489660903, 7247757286, 15032385509, 31138512868, 64424509411, 133143986146, 274877906913, 566935683040, 1168231104479

Offset: 0

Author

Adeniji, Adenike and Samuel Makanjuola (somakanjuola(AT)unilorin.edu.ng) Apr 14 2011

Keywords

• nonn
• easy

Comments

Number of elements in the semigroup IDT_n.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Crossrefs

Cf. A000337, A188377, A188947.

Programs

Magma

[n + (n-1)*(2^n-2): n in [0..50]]; // Vincenzo Librandi, May 01 2011

Mathematica

Table[n+(n-1)(2^n-2),{n,0,40}] (* or *) LinearRecurrence[{6,-13,12,-4},{1,1,4,15},40] (* Harvey P. Dale, Aug 03 2024 *)

PARI

a(n)=(n-1)<Charles R Greathouse IV, Apr 06 2012

Formula

From Colin Barker, Apr 06 2012: (Start)

a(n) = 6*a(n-1)-13*a(n-2)+12*a(n-3)-4*a(n-4).

G.f.: (1-5*x+11*x^2-8*x^3)/((1-x)^2*(1-2*x)^2). (End)

a(n) = A000337(n) - (n-1). - Andrew Penland , Mar 24 2016

E.g.f.: exp(x)*(2 - x + exp(x)*(2*x - 1)). - Stefano Spezia, Apr 10 2022

Extensions

Edited by N. J. A. Sloane, Apr 23 2011

Offset changed from 1 to 0 by Vincenzo Librandi, May 01 2011