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

0,3

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).

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

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 *)

Prog

(Magma) [n + (n-1)*(2^n-2): n in [0..50]]; // Vincenzo Librandi, May 01 2011
(PARI) a(n)=(n-1)<<n-n+2 \\ Charles R Greathouse IV, Apr 06 2012

Crossrefs

Cf. A000337, A188377, A188947.

Sequence in context: A152116 A195688 A111038 * A100506 A173414 A307075

Adjacent sequences: A188713 A188714 A188715 * A188717 A188718 A188719

Keyword

nonn,easy

Author

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

Extensions

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

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

Status

approved