OFFSET
1,1
COMMENTS
Order preserving identity difference partial one - one transformation semigroup, OIDI_n is defined if for each transformation, alpha, x<= y implies xalpha <= yalpha, for all x,y in X_n (set of natural numbers) and also the absolute value of the difference between max(Im(alpha)) and min(Im(alpha)) is less than or equal to one with non-isolation property.
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
G.f.: -x*(-2+4*x-6*x^2+x^3) / (x-1)^4. - R. J. Mathar, Jun 20 2011
E.g.f.: 4*(-2 + (2 + 2*x + x^2 + x^3)*exp(x)). - G. C. Greubel, Jan 13 2018
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, Apr 23 2021
EXAMPLE
For n = 4, a(4) = (4^3-2*4^2+3*4+2)/2 = 46/2 = 23.
MATHEMATICA
Table[(n^3-2*n^2+3*n+2)/2, {n, 1, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 4, 10, 23}, 50] (* G. C. Greubel, Jan 13 2018 *)
PROG
(Magma) [(n^3-2*n^2+3*n+2)/2: n in [1..50]]; // Vincenzo Librandi, May 07 2011
(PARI) a(n)=(n^3-2*n^2+3*n+2)/2 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adeniji, Adenike and Samuel Makanjuola(somakanjuola(AT)unilorin.edu.ng), Apr 30 2011
STATUS
approved