OFFSET
1,1
COMMENTS
The original definition was "Identity difference partial one - one transformation semigroup is a semigroup having the property that the difference between max im(alpha) and min im(alpha) is not greater than 1. This is denoted by S = IDI_n for each n." [Needs editing.]
For all n >= 3, a(n) expressed in base n has the three digits n-2, 2, and 1; for example, a(16) in hexadecimal is "E21". For all n >= 3, a(n+1) expressed in base n is "1112". For all n >= 7, a(n+2) expressed in base n is "1465". - Mathew Englander, Jan 07 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (n+1) + n*(n-1)^2 = n^3 - 2*n^2 + 2*n + 1 = 1 + A053698(n-1).
G.f.: ( -x*(-2 + 3*x - 8*x^2 + x^3) ) / ( (x-1)^4 ). - R. J. Mathar, Apr 14 2011
E.g.f.: exp(x)*(1 + x)*(1 + x^2) - 1. - Stefano Spezia, Apr 10 2022
MATHEMATICA
A188947[n_] := n^3 - 2*n^2 + 2*n + 1; Table[A188947[n], {n, 1, 42}] (* Robert P. P. McKone, Jan 31 2021 *)
PROG
(Magma) [n^3 - 2*n^2 + 2*n + 1: n in [1..30]]; // Vincenzo Librandi, May 01 2011
(PARI) a(n)=n^3-2*n^2+2*n+1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adeniji, Adenike, Apr 14 2011
EXTENSIONS
Edited by N. J. A. Sloane, Apr 23 2011
STATUS
approved