A189890 a(n) = (n^3 - 2*n^2 + 3*n + 2)/2.

2, 4, 10, 23, 46, 82, 134, 205, 298, 416, 562, 739, 950, 1198, 1486, 1817, 2194, 2620, 3098, 3631, 4222, 4874, 5590, 6373, 7226, 8152, 9154, 10235, 11398, 12646, 13982, 15409, 16930, 18548, 20266, 22087, 24014, 26050, 28198, 30461, 32842, 35344, 37970, 40723, 43606, 46622

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

Cf. A188947, A188377.

Sequence in context: A337520 A173185 A294680 * A189587 A345195 A018111

Adjacent sequences: A189887 A189888 A189889 * A189891 A189892 A189893

Keyword

nonn,easy

Author

Adeniji, Adenike and Samuel Makanjuola(somakanjuola(AT)unilorin.edu.ng), Apr 30 2011

Status

approved